Refraction Spherical Surface

Derivation of the equation for Spherical Surface. Is Refraction through a Spherical surface same as the refraction through a Plane surface ?

Q1

Identify True and False statement a) The equation is vaild for plane surfaces b) In the above equation, m1 is the medium in which the object is placed and m2 is the medium in which the image is formed

Q2

A transparent sphere of radius R and refractive index 3/2 is placed in air. a) Image of an object placed at the center of sphere is formed at infinity. True / False ? b) Find the position of Image for 2 positions of object as seen in the figure c) if the object appears to be at a distance of R/4 from the surface when observed along a diameter, find the true position of the object. d) If the radius of sphere is 5 cm and object is placed at a distance 2 cm left to the center. Find the image as seen by an observer standing i) to the left of sphere ii) to the right of sphere

Q3

A beam of parallel rays is incident on a solid transparent sphere of index of refraction m. Find the refractive index of sphere, if a) if a point image is formed at the back of the sphere (as shown in figure) b) a point image is formed at the center of the sphere

Q4

i) A hemisphere has a radius of curvature of 8 cm and an index of refraction of 2. On the axis midway between the plane and spherical surface is a small object. Find the apparent depth of object for the observer looking at the object through a) plane surface b)curved surface Repeat the above question of the entire setup is immersed in a liquid of refractive index equal to c) 1.5 d) 3 ii) Find the position of image as seen by the observer on left and right

Q5

A spherical refracting surface with radius R separates a medium having refractive index 5/2 from air. An object is moving towards the surface from infinity along the principle axis in air. For what positions of the object will a real image be formed ? Repeat the above question, if the refractive indices in the above case are swapped and the object is moving towards the surface from infinity along the principle axis in medium with refractive index 2.5

Q6

i) A spherical surface of radius R separates two media of refractive indices m1 and m2, as shown in figure. Where should an object be placed in medium 1 so that a real image is formed in medium 2 at the same distance ? ii) A spherical surface of radius of curvature R, separates oil ( refractive index 2 ) from glass ( refractive index 1.5 ). The centre of curvature is in oil. A point object placed in glass is found to have a real image in oil. Distance of object and image from the pole is equal. a) Find the distance of object from pole. b) If oil is replaced with air ( refractive index 1 ), is it possible to have the object and image at the same distance ? c) In part ( b ), is it possible with a virtual object ?

SS Magnification

Lateral magnification due to refraction through a spherical surface. Is there any similarity between the equation of magnification due to a spherical mirror and spherical refracting surface ?

Q7

i)A sphere of radius R made of material of refrective index m2 is placed in a medium of refractive index m1. a) Where should an object be placed so that a real image is formed at the same distance from the sphere on the other side ? b) With the object placed at the above position, the sphere is now cut into half along the perpendicular to principle axis and is silvered on its flat face as shown in figure. Find the new position of image. ii) A ring is placed 1 m in front of a spherical glass ball of radius 25 cm with refractive index 1.5. a) Find the position of the final image of the ring and it\'s magnification. b) If the sphere is now cut into half along the perpendicular to principle axis and is silvered on its flat face as shown in figure. Find the new position of image.

Q8

a) A small object of height 0.5 cm is placed in front of a convex surface of glass ( m = 1.5 ) of radius of curvature 10 cm. Find the height of the image formed in glass. b) If the same real object in part ( a ) is now kept at the position of image formed in part ( a ), find the position and height of image formed in this case c) If a virtual object of same height is now kept at the position of image formed in part ( a ) , find the position and height of image formed in this case

SS Longitudinal Magnification

Longitudinal magnification due to refraction through a spherical surface.

Q9

A ball is kept at a height h above a transparent spherical surface of radius of curvature R and made of a material of refractive index m. At t = 0, the ball is dropped to fall normally on the sphere. Find the speed of the image (formed after refraction) as a function of time for t

Thin Lenses

Formation of Spherical Lenses and Derivation of Lens Makers Formula and Lens Formula. Is there any similarity between the Lens Formula and Mirror Formula ?

Q10

a) There are two spherical surfaces of radii 30 cm and 60 cm. In how many ways these surfaces may be arranged to get different lenses. If all the lenses are made of glass ( m = 1.5 ), find the focal length of each lens. b) Find the focal length of a thin concavo-convex lens with equal radii of curvature.

Q11

All the given lenses have radius of curvatures R1 and R2 and have refractive index ml . Lenses are placed in a medium with refractive index mm . For each lens mark if the lens will be converging or diverging if a) mm < ml b) mm > ml

Q12

Consider a beam of light, parallel to the optical axis, falling on a Convex lens. Will the image spot move if a) The beam is rotated by a small angle back and forth b) Lens is rotated by a small angle back and forth c) Now if a slab placed in the path of a parallel beam is rotated by a small angle back and forth from the vertical orientation

Q13

i) A thin lens of refractive index 1.5 has a focal length of 15 cm in air. When the lens is placed in a medium of refractive index 4/3, its focal length will be _____ cm. ii) A thin convex lens ( m = 3/2 ) has focal length f. When measured in two different liquids having refractive indices 4/3 and 5/3, it has the focal lengths f1 and f2, respectively. The correct relation between the focal lengths is a) f1 = f2 < f b) f1 > f and f2 becomes negative c) f2 > f and f1 becomes negative d) f1 and f2 becomes negative iii) Find the refractive index of a medium in which focal length of a convex lens will be negative of its focal length in air.

Q14

i) What is the relation between the refractive indices m1 and m2 ? ii) A hollow concave lens is made of very thin transparent material. It can be filled with air or either of two liquids L1 or L2 having refracting indices n1 and n2 respectively ( n2 > n1 > 1 ). The lens will divegre a parallel beam of light if it is filled with a) air and placed in air b) air and immersed in L1 c) L1 and immersed in L2 d) L2 and immeresed in L1 iii) A concave lens of glass, refractive index 1.5 has both surfaces of same radius of curvature R. On immersion in a medium of refractive index 1.75, it will behave as a a) convergent lens of focal length 3.5 R b) convergent lens of focal length 3 R b) divergent lens of focal length 3.5 R a) divergent lens of focal length 3 R iv) A concave lens made of water ( m = 1.33 ) is placed inside a glass slab ( m = 1.5 ). For an object placed between f and 2f ( measured inside the glass slab ), image is a) virtual, erect, diminished b) real, inverted, and magnified c) virtual, inverted, magnified d) real, inverted, diminished i) A double-convex lens is to be made of glass with an index of refraction of 1.5. One surface is to have twice the radius of curvature of the other and the focal length is to be 60 cm. What is the a) smaller and b) larger radius ? ii) Two thin glasses of radii of curvature 10 cm and 30 cm are joined at the edges to form an air convex lens. a) What is its focal length in air and water ? b) Is it convergent or divergent in water ?

Q15

i) A double-convex lens is to be made of glass with an index of refraction of 1.5. One surface is to have twice the radius of curvature of the other and the focal length is to be 60 cm. What is the a) smaller and b) larger radius ? ii) Two thin glasses of radii of curvature 10 cm and 30 cm are joined at the edges to form an air convex lens. a) What is its focal length in air and water ? b) Is it convergent or divergent in water ?

Ray Diagrams 1

Ray Diagram for an object placed on the axis of lens. Is the image formed by the Lens just a flipped version of the image formed by a spherical Mirror ? Watch the video to see the interesting similarity.

Q16

a) Does focal length of a spherical mirror depends on the medium around it ? b) Does focal length of a spherical lens depends on the medium around it ? c) Does the focal length and radii of curvatures of lens has a simple relation like that for a spherical mirror ? d) Is it possible that a converging lens in one medium is a diverging lens in another medium ?

Q17

What is the relation between the refractive indices m1 , m2 , m3 and m4 if the behavior of light rays is as shown in the figure.

Q18

a) An image I is formed of point object O by a lens whose optic axis ( dashed line ) is as shown in figure. Draw a ray diagram to locate the lens and its focus. If the same image is formed by a spherical mirror ( having the same optic axis ) instead of lens, draw another ray diagram to locate the mirror and its focus. b) For an object placed along the optical axis of the following mirrors/lenses, mark if the image can be Real, Virtual, Magnified, Diminished

Ray Diagrams 2

Ray Diagram for an extended object. Is the image formed by the Lens just a flipped version of the image formed by a spherical Mirror ? Is the nature of Image formed by the Lens and Mirror exactly the same ? Watch the video to see the interesting similarity.

Q19

Which of the rays shown in the figures are not correct ? A converging lens is used to form an image on a screen. When the lower half of the lens is covered by an opaque screen, a) half of image will disappear b) complete image will be formed c) intensity of image will increase d) intensity of image will decrease

Q20

a) Object placed between optic center and 1st principal focus of a diverging lens b) Object placed between optic center and 1st principal focus of a converging lens c) Object placed between optic center and 2nd principal focus of a diverging lens d) Object placed between optic center and 2nd principal focus of a converging lens p) Image is inverted q) Image is erect r) Image is of greater size than the object s) Image is of smaller size than the object

Lenses Magnification

Lateral and Longitudinal magnification due to a lens. Is there Newton?s formula for Lenses ? Is the magnitude of magnification the same for two objects placed at equal distances from the focus ? Watch the video to see striking similarity between Lenses and Spherical Mirrors.

Q21

i) Can a single lens ever form a real and erect image? ii) A diminished image of an object is to be obtained on a screen 1 m from it. This can be achieved by placing a) a plane mirror b) a convex mirror with f > 0.25 m c) a convex lens with f < 0.25 m d) a concave lens with f < 0.25 m iii) Which ones can form a virtual and erect image for all positions of object ? a) convex lens b) concave lens c) convex mirror d) concave mirror iv) A lens forms a virtual, diminished image of an object placed at 2 m from it. The size of image is half of the object. Nature and focal length of the lens ? a) concave, | f | = 1 m b) convex, | f | = 1 m c) concave, | f | = 2 m d) convex, | f | = 2 m v) When an object is placed 15 cm from a lens, a virtual image is formed. Mark the correct statements a) the lens may be convex or concave b) if the lens is diverging, the image distance has to be less than 15 cm c) if the lens is converging, then its focal length has to be greater than 15 cm d) all the above. vi) The distance between a real object and its real image formed by a single lens cannot be less than 4f. True / False ?

Q22

i) A virtual image larger than object can be produced by a) Convex mirror b) Concave mirror c) Diverging lens d) Converging lens ii) If a convergent beam of light passes through a diverging lens, the result may be a a) convergent beam b) divergent beam c) parallel beam iii) When the object is moved slightly closer to a converging lens, the image may a) increase in size and move closer to the lens b) increase in size and move farther away from the lens c) decrease in size and move closer to the lens d) decrease in size and move farther away from the lens

Q23

A real object is placed at focus of an equi-biconvex lens placed in air. In each statement of column I, some changes are made to situation given above. Match the statements in column I with the information regarding final image in Column II. a. refractive index of the lens is doubled p. final image is real b. radius of curvature is doubled q. final image is virtual c. a glass slab is introduced between the object and lens r. final image becomes smaller in size in comparison to size of image before the change was made d. both lens and object are placed in medium of ref index more than 1 s. final image is of same size as the object

Q24

a) A candle is placed 15 cm in front of a lens. If the image of the candle captured on a screen is magnified two times, calculate the focal length and nature of lens. b) A real object is placed 1 cm above the principal axis of a convex lens of focal length of 40 cm. Object distance is 60 cm. If the object now starts moving perpendicularly away from optical axis with a speed of 10 cm/s, then what is the speed of the image ? What will be the speed of image when the object is 2 cm above the axis ?

Q25

i) When an object is at a distance x1 and x2 from the optical center of a lens, virtual and real images are formed respectively, with the same magnification. The focal length of the lens is a) x1 + x2 b) ( x1 + x2 ) / 2 c) x1 + x2 / 2 d) x1 x2 ii) The magnification of an object placed in front of a convex lens is +2. The focal length of the lens is 2 meters. Find the distance (in meters) by which object has to be moved to obtain a magnification of - 2

Lens Displacement Method

Lens Displacement Method for measuring the focal length of a Convex Lens.

Q26

An object and a screen are a fixed distance D apart. A converging lens of focal length f is placed between the object and screen. A real image of the object is formed on the screen for two positions of lens which are separated by a distance d. a) write the focal length of lens in terms of D and d b) write d in terms of D and f c) write the expression for magnification in each position of lens, m1 and m2, in terms of D and d d) what will be the ratio of heights of image formed in closer position of lens (from object) to that in farther position of lens (from object) e) focal length of lens in terms of m1 and m2 will be

Q27

i) An object is placed at a certain distance from a screen. A convex lens of focal length 20 cm is placed between the screen and the object. A real image is formed on the screen for two positions of the lens, which differ by a distance of 30 cm. What is the distance of the object from the screen? ii) The distance between an object and a screen is D = 1 m. A convergent lens of focal length f = 21 cm is placed between the object and the lens such that a sharp image of the object is formed on the screen for 2 positions of lens. a) find the positions of lens from the object b) ratio of heights of images h1 & h2 in the 2 cases c) if the sizes of images are 4.5 cm and 2 cm, then find the size of object

Graphical Representation

Graphical Representation of the Position of Image vs Position of Object formed by Lenses

Q28

Mark the correct u-v graph for Convex lens, Concave lens, Concave mirror and Convex mirror using cartesian sign conventions

Power

Definition of Optical Power. Please be careful about the most common mistake made while using this equation.

Q29

i) A concave lens has a focal length of 25 cms. What is the power of lens ? ii) If the radius of curvature of each surface of an equiconvex lens is changed from 5 cm to 6 cm, then the power a) remains unchanged b) increases c) decreases

Q30

A lens has a power of +5 diopters in air. What will be its power if completely immersed in water ? ( amw = 4/3 and amg = 3/2 )

Lens with Different Mediums

If a lens has different mediums on its either side, will its focal length be the same on both sides ? Will its Image focus and Object focus be at the same distance from the lens ?

Q31

Match the relationship between m1, m2 and m3 in column I to the ray diagrams shown in Column II.

Combination of Lenses

Equivalent Lens for a combination of lenses

Q32

a) A convex lens of power +6 dioptre is placed in contact with a concave lens of power -4 dioptre. What will be the nature and focal length of this combination? b) A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. Find the power of the combination. c) Find the nature and focal length of a lens which must be placed in contact with a concave lens of focal length 25 cm in order that the lens combination may produce a real image of an object placed at infinity. d) Find the lateral magnification produced by the combination of lenses shown in figure.

Q33

i) An equi-convex lens of glass of focal length f is cut into two parts in two different ways as shown in figure.Find the focal length and power of each part after cut in both cases. ii) An equi-convex lens is broken into four parts and rearranged as shown. If the initial focal length is f, then find the equivalent focal length of the given combination of parts. iii) You are given two identical plano-convex lenses. When you place an object 20 cm to the left of a single plano-convex lens, the image appears 40 cm to the right of the lens. You then arrange the two plano-convex lenses back to back to form a double convex lens. If the object is 20 cm to the left of this new lens, what is the new location of the image ? iv) A convex lens of glass ( m = 1.5 ) is formed by combining two surface of radii R1 = 60 cm and R2 = 30 cm. It is cut into two parts in two different ways as shown in part (i). Find the focal length of each part.

Q34

The radius of curvature of all curved surfaces is r and the refractive index of all the lenses is 1.5. Find the focal length of the combination of lenses shown below ?

Q35

i) Two thin plano-convex lenses are placed together with their plane surfaces in contact. Lenses are made of different materials of refractive indices m1 and m2 and but have the same radius of curvature of the curved surfaces which is equal to R. a) Find the focal length of the combination. b) Repeat the above problem if the lenses are plano-concave instead of plano-convex c) Repeat the above problem if one lens is plano-concave and the other is plano-convex, with their curved surfaces in contact ii) A bi-convex lens is formed with two thin plano-convex lenses with their plane surfaces in contact. Refractive index of first lens is 1.5 and that of the second lens is 1.2. Both the curved surface are of the same radius of curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, find the image distance(s).

Lens Mirror Combination

Does a combination of lenses and mirror act as a Lens or a Mirror ? What is the Power of a lens and mirror combination ?

Q36

Find the nature and focal length of the equivalent mirror for all the cases given below.

Q37

i) A plano-convex lens with radius R and refractive index m is silvered on its plane side. Where should an object be placed if its image is to coincide with itself ? ii) A plano-convex lens is silvered on its a) plane side b) curved side then in which case is the radius of curvature of equivalent mirror higher ? iii) A plano-convex lens when silvered on the plane side behaves like a concave mirror of focal length 60 cm. However, when silvered on the convex side, it behaves like a concave mirror of focal length 20 cm. Find the refractive index of the lens.

Q38

i) A point object is placed at a distance of 20 cm from a thin planoconvex lens of focal length 15 cm. The place surface of the lens is now silvered. The image created by the system is at a) 24 cm to the left of the system b) 24 cm to the right of the system c) 12 cm to the left of the system d) 12 cm to the right of the system ii) An object is placed 1 m in front of the curved surface of a plano-convex lens whose plane surface is silvered. A real images is formed in front of the lens at a distance of 120 cm then, the focal length of the lens is a) 99.1 cm b) 121.5 cm c) 109.1 cm d) 130.5 cm

Human Eye

Anatomy of Human Eye. How does a human eye focus the objects placed at different distances ?

Glasses

Why are some people not able to see clearly ? How do Glasses rectify the common defects of vision ?

Q39

Given that the distance of retina from eye-lens is about 2.5 cm and minimum distance of distinct vision is around 25 cm. i) Minimum focal length of eye lens of a normal person is a. 25/9 cm b. 2.5 cm c. 25/11 cm d. 25/12 cm ii) Maximum focal length of a eye lens of a normal person is a. 25/9 cm b. 2.5 cm c. 25/11 cm d. 25/12 cm iii) A near sighted man can clearly see objects only up-to a distance of 100 cm. Number of the spectacles lenses to correct this defect will be a. - 1 b. 1 c. - 3 d. 3 iv) A far sighted man cannot see objects clearly unless they are at least 150 cm from his eye. The number of the spectacle lenses that will make his range of clear vision equal to an average grown up person will be a. - 0.66 b. 0.66 c. - 3.33 d. 3.33

Apparent Size

Why do objects closer to us appear to be bigger ?

Q40

An object of height h1 = 9 ft is placed at a distance d1 = 3 m from the eye. Another object of height h2 = 12 ft is placed at a distance d2 = 6 m from the eye. Which object appears bigger to the eye ?

Simple Microscope

How does a Simple Microscope magnify ?

Q41

i) A man is looking at a small object placed at his near point. Without altering the position of his eye or the object, he puts a simple microscope of magnifying power 4 X before his eyes. The angular magnification achieved is a) 4 b) 3 c) 2 d) 1 ii) An object is placed at a distance u from a simple microscope of focal length f. The angular magnification obtained depends a) on f but not on u b) on u but not on f c) on f as well as u d) neither on f nor on u iii) To increase the angular magnification of a simple microscope, one should increase a) the focal length of lens b) the power of lens c) the aperture of lens d) the object size

Q42

A small object is placed at a distance of 3.6 cm from a magnifier of focal length 4 cm. a) Find the position of the image. b) Find the linear magnification. c) Find the angular magnificat ion. Take D = 25 cm

Compound Microscope

Basic construction and functioning of a Compound microscope.

Q43

i) In a compound microscope, the intermediate image is a) virtual, erect and magnified b) real, erect and magnified c) real, inverted and magnified d) virtual, erect and reduced ii) Focal length of the objective of a compound microscope is fo and its distance from the eyepiece is L. The object is placed at a distance u from the objective. For proper working of the instrument, a) L < u b) L > u c) fo < L < 2fo d) L > 2fo

Q44

i) Focal lengths of the objective and eyepiece of a compound microscope are 2 cm and 3 cm respectively. Distance between the objective and eyepiece is 15 cm. Final image formed by the eyepiece is at infinity. Find the distance of object and image ( formed by objective ), measured from the objective lens. Least distance of distinct vision is 24 cm. ii) A compound microscope has an objective of power 100 D and an eyepiece of power 40 D. An object has to be placed at a distance of 1.2 cm away from the objective for normal adjustment. a) Find the angular magnification. b) Find the length of the microscope tube.

Q45

The separation L between the objective ( f = 1 cm ) and the eyepiece ( f = 6 cm ) of a compound microscope is 14.8 cm. Least distance of distinct vision is 24 cm Where should a small object be placed so that the eye i) is least strained to see the image ii) is maximum strained to see the image Find the angular magnification produced by the microscope in each case. iii) Find the position of object so that the angular magnification is 20

Telescope

Basic construction and functioning of a Telescope. What is the difference between an Astronomical Telescope and a Terrestrial Telescope ?

Q46

i) A planet is observed by an astronomical refracting telescope having an objective of focal length 16 m and an eyepiece of focal length 2 cm. a) Find the distance between the objective and eyepiece and the angular magnification b) Is the image of planet inverted ? ii) An astronomical telescope has an angular magnification of magnitude 5 for far object. The separation between the objective and the eyepiece is 36 cm and the final image is formed at infinity. Find the focal length of objective and eyepiece. iii) The eyepiece of an astonomical telescope has a focal length of 10 cm. The telescope is focussed for normal vision of distant objects when the tube length is 1 m. Find the focal length of the objective and the magnifying power of the telescope.

Chromatic Aberration

Chromatic Aberration due to Lenses. And how to rectify Chromatic Aberration ?

Q47

i) Which one of the following spherical lenses does not exhibit dispersion? Radii of curvature of the surfaces of the lenses are as given in the diagrams ii) The focal length of a convex lens for blue and red colors of light are fB and fR, respectively, and those of a concave lens are FB and FR then a) fB > fR and FB < FR b) fB < fR and FB > FR c) fB > fR and FB > FR d) fB < fR and FB < FR iii) A parallel beam of white light fall on a combination of a concave and a convex lens, both of the same material. Their focal lengths are 15 cm and 30 cm respectively for the mean wavelength in white light. On the same side of the lens system, one sees coloured patterns with violet color nearer to the lens. True / False

Q48

i) The dispersive powers of two lenses are 0.01 and 0.02. If focal length of first lens is + 10 cm, then what should be the focal length of the second lens, so that they form an achromatic combination ? ii) A combination is made of two lenses of focal lengths f and f\' in contact ; the dispersive powers of the materials of the lenses are w and w\' . The combination is achromatic when : a) w = wo, w\' = 2 wo, f\' = 2f b) w = wo, w\' = 2 wo, f\' = f / 2 c) w = wo, w\' = 2 wo, f\' = - f / 2 d) w = wo, w\' = 2 wo, f\' = - 2f iii) The dispersive power of crown and flint glasses are 0.02 and 0.04, respectively. An achromatic converging lens of focal length 40 cm is made by keeping two lenses, one of crown glass and the other of flint glass, in contact with each other. Find the focal lengths of the two lenses

Q49

i) Spherical aberration in a thin lens can be reduced by a) using a monochromatic light b) using a doublet combination c) using a circular annular ring over the lens d) increasing the size of the lens ii) A real image of a distant object is formed by a plano-convex lens on its principal axis. Spherical aberration a) is absent b) is smaller if the curved surface of the lens faces the object c) is smaller if the place surface of the lens faces the object c) is the same whichever side of the lens faces the object

1

a) A parallel beam of light travelling in water (refractive index = 4/3) is refracted by spherical air bubble of radius 2 cm in water. Find the position of the image due to refraction at the first surface and the position of the final image. Consider the light rays to be paraxial. b) If the above setup is now surrounded by a medium of refractive index 1.5 as shown in figure, find the position of final image as seen by observer.

2

In the figure shown, a point object is placed in air. The spherical boundary shown has radius of curvature 1 meter. Refractive index above the principle axis AB is 1.6 and below AB is 2. How many images will be formed ? Find the separation between the images.

3

i) A glass sphere of radius R, refractive index 1.5 has a spherical cavity of radius R/2, concentric with it. a) A narrow beam of parallel light is directed into the sphere. Locate the final image. b) Find the position of image of a spot on the inner surface of the hollow sphere when viewed from the left and right. ii) A glass sphere of radius R, refractive index 1.5 has a spherical cavity of radius R/2, as shown in figure. a) Find the position of an object placed at the center of cavity, when viewed from left and right. b) Find the position of image of a spot at the center of outer sphere, when viewed from the left and right.

4

a) Half the surface of a transparent sphere of refractive index 1.5 is silvered. A narrow, parallel beam of light is incident on the unsilvered surface, symmetrically with respect to silvered part. Find the final position of image formed after refraction, reflection from the mirror and final refraction from the surface of sphere.. b) A small object is placed inside the solid glass sphere of radius 20 cm. The refractive index of glass is 1.5. The position of object is at a distance 5 cm from center. If right half of sphere is polished, find the distance between the images seen by observer on the left side of sphere. Assume paraxial rays conditions are satisfied.

5

a) Figure shows 2 thin parallel beams of light incident on a hemisphere of radius R and refractive index = 2 Red ray is such that its angle of incident on the plane surface is equal to the critical angle for the hemisphere-air interface ( qc = 30o ) What will be the path of Violet and Orange beams ? b) If the rays were incident as shown, what will be the path of Violet and Orange beams ?

6

Find the position of image as seen by observer in the 2 cases.

7

a) A quarter cylinder of radius R and refractive index 1.5 is placed on a table. A point object is kept at a distance mR from it. Find the value of m for which a ray from the object will emerge parallel to the table as shown in fig. b) Figure shows as irregular block of material of refractive index 2. A ray of light strike the face AB as shown in the fig. After refraction it is incident on a spherical surface CD of radius of curvature 0.4 m and enters a medium of refractive index 1.514 to meet PQ at E. Find the distance OE upto two places of decimal .

8

A source is placed 30 cm from a convex lens which has a focal length of 20 cm. The source is initially located on the axis of the lens. a) The lens is then cut into two halves in a plane along the principal axis and the two halves are separated by a distance of 4 mm ( each half 2 mm on each side ) along the perpendicular to the pricipal axis. What will be the location and size of the image(s) ? b) If the middle 4 mm of lens is cut out but the remaining portions are not moved, find the location of image(s). c) If the middle 4 mm of lens is cut out and the remaining portions are separated by a distance of 4 mm ( 2 mm on each side ) , find the location of image(s).

9

a) A layered convex lens is made of two kinds of glasses. How many images will be produced by the lens for an incident beam parallel to the optical axis? Neglect the reflection and refraction of light at the boundaries between layers. b) A parallel beam of light falls on the surface of a convex lens whose radius of curvature of both sides is R. Refractive index of the material of the lens varies as m = 1.5 + 0.5 r , where r is the distance of the point on the aperture from the optical center in cm. Find the length of the region on the axis of the lens where the light will appear. The radius of aperture of the lens is 1 cm.

10

a) A convex lens focuses an object 40 cm from it on a screen placed 10 cm away from it. A glass plate ( m = 1.5 ) and of thickness 3 cm is inserted between the object and the lens. Where should the object be placed so that its image is again focused on the screen ? b) A convex lens of focal length 30 cm forms a sharp image of an object on a screen placed at a distance 90 cm from the lens. Now the screen has been displaced 30 cm towards the lens. By what distance should the object be shifted in order to obtain a sharp image on the screen?

11

Find the nature and position of the final image and also its length. Assume that each lens is a thin lens. Will the image be Longitudinally Inverted ?

12

Two point sources S1 and S2 are 24 cm apart. Where should a convex lens of focal length 9 cm be placed in between them so that the images of both sources are formed at the same place ?

13

i) The apparent thickness of a thick plano-lens (convex or concave) is measured once with the plane face upward and then with the convex face upward. Apparent thickness will be a) more with plane face up for plano-convex lens b) more with plane face up for plano-concave lens c) more with curved face up for plano-convex lens d) more with curved face up for plano-concave lens e) same in the two cases for both plano-convex and plano-concave lens f) any of the above depending on the value of its actual thickness ii) A plano-convex lens has a thickness of 4 cm. When placed on a horizontal table, with the curved in contact with it, the apparent depth of the bottom most point of the lens is found to be 3 cm. It the lens is inverted such that the plane face is in contact with the table, the apparent depth of the center of the plane face is found to be 25/8 cm. Find the focal length of the lens. Assume the lens to be thin while finding its focal length.

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i) The focal length of a thin convex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from m25 to m50. The ratio is ? ii) A point source is placed on the axis of a convex lens of focal length 20 cm at a distance of 40 cm. If the lens is raised by 1 cm, by how much will the image be lifted relative to the previous axis ?

15

Optical axis of a thin equiconvex lens is the x axis. The coordinates of a point object and its image are ( - 40 cm, 1 cm) and ( 50 cm, - 2 cm) respectively. a) What is the location of lens ? b) What is the focal length of lens ? c) Where are their image focus and object focus located ?

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A lens forms the image of an object such that the distance between the object and image is 10 cm and the magnification produced is + 1/4. Find the focal length of lens and position of object.

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a) An object is viewed through a convex lens of focal length 10 cm. Its image is erect and magnified 2 times. How far is the object from the lens? b) Image of a real object formed by a plano-convex lens is 8 m behind the lens, is real and is one-third the size of object. The wavelength of light inside the lens is 2/3 times the wavelength in free space. Find the radius of the curved surface of lens.

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i) The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image. ii) When an object is placed at the proper distance to the left of a converging lens, the image is focused in a screen 30 cm to the right of lens. A diverging lens is now placed 15 cm to the right of the converging lens and it is found that the screen must be moved 5 cm farther to the right to obtain a sharp image . Find the focal lenght of the diverging lens.

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a) Two convex lenses of focal lengths 20 cm and 10 cm are placed 25 cms apart. For parallel incident rays on the lens with focal length of 20 cm, find the position of image formed by the second lens. b) Now the above two lenses are placed 5 cms apart. An object is placed at a distance of 10 cm to the left on the axis of lens of focal length 20 cm. Find the position of the image formed by the second lens and its magnification.

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a) An extended object of size 2 mm is placed on the principal axis of a converging lens of focal length 10 cm. It is found that when the object is placed perpendicular to the principal axis the image formed is 4 mm in size. The size of image when it is placed along the principal axis is ..................... mm. b) A linear object AB is placed along the axis of a convex lens with focal length = f. The object is moving with speed V. The speed of the image of both points A and B is 4V. Find the length of object in terms of the focal length of lens.

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i)A thin plano-convex lens of focal length f is split into two halves which are placed at different distances from object such that both halves form a sharp image of the object at the screen. Separation between object and screen is 1.8 m. Magnification of image formed by one of the half lens is 2. Find the focal length of lens and separation between the halves. ii) In Lens Displacement method, the distance between object and screen is 96 cm. The ratio of length of two images formed by a converging lens placed at 2 positions between them is 4. Find the, a) ratio of length of object to the length of shorter image b) distance between the two positions of lens c) focal length of the lens

22

i) A convex lens of focal length 20 cm and a concave lens of focal length 5 cm are kept along the same axis with a distance d between them. If a parallel beam of light falling on Convex lens, leaves Concave lens as parallel beam, then find d. ii) Repeat the above question if Concave lens is replaced with a Convex lens of same focal length. iii) A convex lens of focal length f1 and a concave lens of focal length f2 are kept along the same axis with a distance d between them. Concave lens is on right of Convex lens. Where should a real object be placed on the axis of convex lens A (on its left), so that the image formed by the Concave lens B remains at the same position wrt lens B.

23

Two thin convex lenses of focal lengths f1 and f2 are separated by a horizontal distance d ( where d < f1 , d < f2 ) and their centres are displaced by a vertical separation D as shown in the figure. Taking the origin at the centre of the first lens, find the x and y coordinates of the image for a parallel beam of rays coming from the left.

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Four combinations of a thin lens ( all with f = 10 cm ) and a spherical mirror are shown in the figure below. In each case where should a real point object be placed in front of the lens so that its images after refraction from lens, reflection from mirror and then refraction from lens coincides with itself ?

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i) Final image after two refractions through the lens and one reflection from the mirror coincides with the object. Refractive index of the material of the lens m = 3/2. Find d. ii) Final image after two refractions through the lens and one reflection from the mirror coincides with the object. Refractive index of the material of the lens m = 3/2. Find d. iii) A converging lens of focal length f1 is placed in front of and coaxially with a concave mirror of focal length f2. Their separation is d. A parallel beam of light incident on the lens returns as a parallel beam from the arrangement. Mark the correct statements. a) diameters of the incident and returning beams will be same b) d = f2 ? 2 | f2 | c) d = f1 ? | f2 | d) if the entire arrangement is immersed in water, the conditions will remain unaltered.

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Find the position ( relative to the lens ) of final image formed by the system

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i) When medium on both sides of lens has refractive index m1 , focal length of a thin lens is f1. Now medium on one side of the lens is replaced by a medium of refractive index m3. The radius of curvature of the surface of lens, in contact with the new medium, is R2. Find the focal length of lens for the parallel rays incident from a) medium 1 b) medium 2 ii) Focal length of a thin lens in air is 10 cm. Now, medium on one side of the lens is replaced by a medium of refractive index m = 2. The radius of curvature of the surface of lens, in contact with the medium, is 20 cm. Find the focal length of lens for the parallel rays incident from a) air b) medium iii) An equi - convex lens of focal length 20 cm, made of glass of refractive index 1.5, has water ( m = 1.33 ) on one side and air on the other. An object is placed 15 cm from the lens on the side with water. Where is the image formed ?

28

a) In the figure, a thin lens with refractive index m2 has different mediums on its either side. For the light incident on it from both sides, find the focal lengths of lens. The radius of curvature for both the surfaces is R. b) A transparent thin film of refractive index n1 = 1.4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n2 = 1.5 as shown in the fig. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f1 from the film, while rays of light traversing from glass to air get focused at ditance f2 from the film. Then

29

A lens is made of three thin different mediums as shown in figure. For an object, a real image is formed at a distance of 10 cm from the lens. Find a) the position of object b) A slab of thickness 1.5 cm and refractive index 1.5 is introduced between the image and the lens. Find new position of object so that image formed after refraction through the slab is again formed at the same point ( 10 cms from the lens )

30

i)A convex lens is in contact with concave lens. The magnitude of the ratio of their focal length is 3/2. Their equivalent focal length is +30 cm. What are their individual focal lengths? ii) Two thin symmetrical lenses of different nature and of different material have equal radii of curvature R = 15 cm. The lenses are put close together and immersed in water ( mw = 4/3 ). Their equivalent focal length is +30 cm. Find the difference between their refractive indices.

31

i) A thin equiconvex lens ( m = 3/2 ) of focal length 10 cm is cut and separated and a material of refractive index 3 is filled between them. What is the focal length of the combination ? If the entire setup is now immersed in the same liquid, find the focal length of the system inside the liquid? ii) Two equi-concave lenses with same radius of curvature = 20 cm and refractive index 1.5 are placed in contact. Find the effective focal length of the combination. If the combination is now placed inside a liquid of refrective index 1.6 such that the gap between the lenses is filled with a) liquid b) air find the focal length of the system inside the liquid?

32

An equi-concave lens ( ) of radius R is placed in contact with a Concave mirror of radius 3R as shown in figure. Entire setup is now placed inside water of refractive index 4/3, such that gap between the lens and mirror a) is NOT filled with water (still has air) b) is also filled with water Find the effective focal length of the system in water.

33

The convex surface of a thin concave-convex lens of glass of refractive index 1.5 has a radius of curvature 20 cm. The concave surface has a radius of curvature 60 cm. the convex side is silvered and placed on a horizontal surface a) Where should a pin be placed on the optic axis such that its image is formed at the same place ? b) If the concave part is filled with water of refractive index 4/3, find the distance through which the pin should be moved, so that the image of the pin again coincides with the pin.

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i) A point object is placed 10 cm in front of a convex lens of focal length 20 cm and refractive index 1.5. The convex surface of the lens farther away from the pin is silvered and has a radius of curvature of 22 cm. Determine the position of the final image. Is the image real or virtual ? ii) An object in placed 30 cm in front of a concave lens of refractive index 1.5 and has equal radii of curvature of its two surfaces, each 30 cm. The surface of the lens farther away from the object is silvered. Find the nature and position of the final image.

35

A concave mirror is placed on a horizontal table with its axis directed vertically upwards. Let C be its centre of curvature. A point object is placed at C. It has a real image, also located at C. If the mirror is now filled with water 1) the image will be a) real and will remain at C b) real and located at a point between C and c) virtual and located at a point between C and Pole d) real and located at a point between C and Pole 2) By what distance should the object be moved so that its image will again coincide with the object 3) Where should an object be placed if its image is to be captured on a screen and is enlarged by a factor of 2 4) Where should the object be placed so that its image is formed at infinity

36

i) A thin equi-convex lens of radius R and refractive index 3/2 is placed on a horizontal plane mirror. The space between the lens and the mirror is then filled with water of refractive index 4/3 as shown in the figure. It is found that when a point object is placed 15 cm above the lens on its principal axis, the object coincides with its own image. On repeating with another liquid, the object and the image again coincide at a distance 25 cm from the lens. a) Calculate the refractive index of the liquid b) If water is filled upto the height of lens, where should the object be placed so that its image coincides with itself ? ii) A thin equi-convex lens of refractive index 3/2 and radius of curvature 50 cm is placed of a reflecting convex surface of radius of curvature 100 cm. A point object is placed on the principal axis of the system such that its final image coincides with itself. Now, a transparent liquid is filled between the mirror and lens such that final image of the object is at infinity. Find refractive index of the liquid used. Also, find the position of the object.

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a) For a myopic eye, the far point is 80 cm. Calculate the power of the lens required to correct the defect. b) A boy with his spectacles consisting of concave lens of focal length 1 m can see clearly the objects lying at a distance of 25 cm. How far should he keep a newspaper from eyes so that he can read it without glasses

38

i) A simple microscope has a magnifying power of 5 when the image is formed at the near point (25 cm) of a normal eye. a) what is its focal length ? b) what will be its magnifying power if the image is formed at infinity? ii) A child has near point at 10 cm. What is the maximum angular magnification the child can have with a convex lens of focal length 10 cm?

39

A compound microscope has a magnifying power of 100 when the image is formed at infinity. The objective has a focal length of 0.5 cm and the tube length is 6.5 cm. Find the focal length of the eyepiece.

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i) The separation between the objective and the eyepiece of a compound microscope can be adjusted between 9.8 cm to 11.8 cm. If the focal lengths of the objective and the eyepiece are 1 cm and 6 cm respectively, find the range of the magnifying power if the image is always needed at 24 cm from the eye. ii) An eye can distinguish between two points of an object if they are separated by more than 0.22 mm when the object is placed at 25 cm from the eye. The object is now seen by a compound microscope having a 20 D objective and 10 D eyepiece separated by a distance of 20 cm. The final image is formed at 25 cm from the eye. What is the minimum separation between two points of the object which can now be distinguished?

41

The eyepiece and objective of a microscope of focal length 3 cm and 4 cm respectively, are separated by a distance of 20 cm. The eye-piece and the objective are to be interchanged such that the angular magnification of the instrument remains same. What is the new separation between the lenses?

42

A telescope has an objective of focal length 50 cm and eyepiece of focal length 5 cm. The least distance of distinct vision is 25 cm. The telescope is focused for distinct vision on a scale 200 cm away from the objective. Calculate: i) the separation between the objective and eyepiece ii) the lateral magnification iii) the angular magnification

43

a) An equi-convex lens of crown glass having radii R1 = 10 cm forms an achromatic combination with a double concave lens of flint glass having radii R1 = 10 cm and R2 = 11 cm. Calculate the ratio of the change in refractive indices of the extreme rays of the visible region in the two glasses. b) A convex lens of crown glass having focal length of 30 cm and a concave lens of flint glass forms an achromatic lens when places in contact. The mean refractive indices for the two glasses are 1.56 and 1.63 respectively and the difference in refractive indices for the extreme rays for these two glasses is respectively 0.014 and 0.021 for two spectral lines. Find the focal length of the concave lens.

44

A thin convex lens of crown glass forms an achromatic lens of focal length 30 cm in contact with a thin concave lens of flint glass. The radius of the crown surface and flint surface in contact is 20 cm. Find the radius of curvature of the second surface of each lens. The dispersive power and mean refractive index are respectively 0.017 and 1.5 for crown glass and 0.034 and 1.7 for flint glass.

45

A stationary observer is looking at a fish ( in water of m = 4/3 ) through a converging lens of focal length 90 cm. At t = 0, the lens is allowed to fall freely from a height of 62 cm with its axis vertical. The fish and the observer are on the principal axis of the lens. The fish is initially at a depth of 44 cm and is moving up with constant velocity 100 cm/s. Find the velocity with which the fish appears to move to the observer at t = 0.2 sec.

46

i) Graph between object distance u and image distance v for a lens is given. Focal length of the lens is a) 5 0.1 b) 5 0.05 c) 0.5 0.1 d) 0.5 0.05 ii) Figure shows variation of magnification \'m\' ( by a thin convex lens ) and position of image \'v\'. Mark the correct statements ? a) Focal length is equal to intercept on v-axis b) Focal length is equal to inverse of slope of line c) Magnitude of intercept on m-axis is equal to unity d) None of the above

47

A convex lens of focal length 15 cm and a concave mirror of focal length 30 cm are kept with their optic axis parallel but separated in vertical direction by 0.6 cm as shown. Find the location of image after refraction from lens and reflection from mirror.

48

a) For the combination of two plano-convex lenses, find the position of the image of the parallel beam of light relative to the common principal axis. b) Now, the second lens is shifted vertically downward by a small distance 5 mm and the extended parts of both lenses are blackened. Find the new position of the images of the parallel beam.

49

An object is approaching a thin convex lens of focal length 0.3 m with a speed of 0.01 m/s. Find the magnitudes of the rates of change of position and lateral magnification of image when the object is at a distance of 0.4 m from the lens.

50

Two thin lenses with same focal lengths ( f ) are placed in contact and form the image of a distant object. If the 2nd lens ( the one on the right ) is moved towards right, then what will be direction of motion of image ? Consider all 4 possible cases and consider that the second lens is moved for a distance more than 3f. Do not use calculus.

51

Two thin lenses with same focal lengths ( f ) are placed in contact and form the image of a distant object. If the 2nd lens ( the one on the right ) is moved towards right, then what will be direction of motion of image ? Consider all 4 possible cases and consider that the second lens is moved for a distance more than 3f. Use calculus.

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