Geometrical Optics Questions and Answers

4 A steel wire is coaxially embedded in a glass tube external diameter of which is much greater than that of the wire Refractive index of the glass is 4 3 If diameter of the steel wire appears 8 3 mm when looked into the glass tube through its curved surface find the actual diameter of the 2 mm steel wire

You use a magnifying glass to focus the sun s light onto a single point and start a fire The magnifying glass must be what kind of lens Converging Orefraction Diverging Concave

A student wants to find the focal length of a magnifying glass The hold the magnifying glass 1 5 meters away from the classroom window and measure how far from the magnifying glass a clear image projects onto a piece of paper The image distance is found to be 0 5 What is the focal length of the lens round to two decimal places Your Answer

A phone is placed at a distance of twice the focal length from a lens What type of image will be produced on the opposite side of the lens that can be projected onto a screen virtual optical convex

09 In which quadrant graph is plotted in case of convex lens and mirror What is the shape of the graph in case of convex lens and concave mirror when graph is plotted between n Le 1 2 v How f can be ser obtained from it

A thin converging lens of focal length f 1 5m is placed along y axis such that its optical center coincides with the origin A small light source S is placed at 2m 0 1m A plane mirror inclined at an angle 0 tan 0 3 is placed at d 0 so that y coordinate of final image is 0 3m Assuming paraxial ray assumption the value of d in m is S AX X

A parallel light beam falls on a lens which is silvered from back side as shown and both surfaces have radius 25 cm then distance in cm from lens where the beam converges on principle axis is x so fill value 16x 25 of

A lensmaker has to design an achromatic combination of effective power 0 8 D The two types of glasses to be used A and B have dispersive powers in the ratio 2 3 Then the lens made from glass B will have focal length

A thin equiconvex lens made of material of refractive index 1 5 has a focal length of 10 cm in air One side of the lens is replaced by a medium B of refractive index 1 3 When a point object is placed in air at a distance of 20 cm from the lens on its principal axis its image is formed at a distance of x cm in the medium B from the lens When the same object is placed in medium B at a distance of 20 cm from the lens on its principal axis its image is formed at a distance of y cm in the air from the lens then O x y Ox 1 3 y Ox 1 3 y O x 1 3 y

The objective of an astronomical telescope has a focal length of 80 cm The telescope is focused for normal vision of distant objects when the tube length is 1 0 m If the focal length of eye piece is fe in cm and magnifying power of telescope is m then the value of fe is m

8 A person with myopia has a far point 60cm from her eye What are the refractive powers of the eyeglasses and contact lenses should she wear Assume distance between eye and glasses of 1 5cm Give your answer in D 1 P glasses 1 67D P contact lens 1 71D 2 P glasses 1 71D P contact lens 1 67D 3 P glasses 1 71D P contact lens 1 67D 4 P glasses 1 71D P contact lens 1 67D

A beam of light coming from infinity is passing through a biconvex lens having radius of curvature R 20 cm of each surface is focused at a certain distance from lens Find the radius of curvature of emergent wave front from lens lens 1 5 A 10 cm C 1 cm B 5 cm D 20 cm

5 A thin lens with refractive power 15D is placed 40cm after an object Find the location and type of image 1 d2 0 06m image is real 2 d2 0 08m image is virtual 3 d2 0 06m image is virtual 4 d2 0 08m image is real

If the polarizing angle of a piece of glass for green light is 54 74 then the angle of minimum deviation for an equilateral prism made of same glass is Given tan 54 74 1 414 A 45 C 60 B 54 74 D 30

A convex lens forms an image of an object placed in its axis on a screen The height of the image is 9 cm Now the lens is displaced until an image is again obtained on the screen The height of the image is 4 cm The distance between the object and the screen is 90 cm It follows that Option A D B C The distance between the two positions of the lens is 30 cm The focal length of the lens is 24 cm The height of the object is 6 cm The distance of the object from the lens in its first position is 36 cm Rate this questio

In given arrangement find the distnace of the image formed by concave mirror of very small aperture from the pole of concave mirror in m All mirrors are placed at 45 with horizontal Given focal length of the concave mirror to be 10 m 10m NIL 10m 10m

7 A thin lens placed 30cm after an object form an image 25cm after it Calculate the object and image vergences and find the lens power 1 U 3 33D V 4 0D P 7 33D 2 U 3 33D V 4 0D P 0 67D 3 U 3 33D V 4 0D P 7 33D 4 U 3 33D V 4 0D P 0 67D

16 When observed from the earth the angular diameter of the sun is 0 5 degree The diameter of the image of the sun when formed in a concave mirror of focal length 0 5 m will be about A 3 0 mm B 4 4 mm C 5 6 mm D 8 8 mm OF REFRACTION REFRACTION AT PLANE SURFACE AND T I R 1000 A The refractive index of the it

7 A double convex lens made of glass if refractive index 1 5 has its both surface of equal radii of curvature of 15 cm each An object of 5cm height is placed at a distance of 12 cm from the lens Find the position nature and size of image

An object 2 0m in front of a lens forms a sharp image on a film 10cm behind the lens A glass plate 1cm thick of refractive index 1 50 is interposed between lens and film with its plane faces parallel to film At what distance from the lens should the object shifted to be in sharp focus on film A B C D 2 0 m 6 4 m 5 6 m 3 2 m

If final image formed after two refractions through the lens and one reflection from the mirror is at the same point O then dis A 100 cm C 90 cm B 110 cm D 80 cm 1 5 J 80 cm 10 cm d 20 cm R 30 cm

A microscope is focussed on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index 1 5 is placed over the mark How should the microscope be moved to get the mark again in focus 1 1 cm downward upward 2 1 cm upward 4 45 unward

A near sighted person wears eye glass with a power of 55 D for distance vision His doctor prescribe a correction of 1 5D in near vision section of his te which is measured relative to main parts of the lens What is the focal length of near vision section of the lens a 18 18 cm b 25 cm c 40 cm d 35 cm Oa OF Od

81 blue green red 7 The fig shows a mixture colours incident on a right angled prism The critical angles of the material of prism for red green and blue colours are 46 44 43 respectively The arrangement will separate B G R 1 Red from Green and Blue 2 Blue from Green and Red 3 Green from Red and Blue 4 All the colo 45

Q 16 A parallel beam of light travelling in x direction is incident on a glass slab of thickness t The refractive index where o is of the slab changes with y as 1 10 1 F the refractive index along x axis and yo is a constant The light beam gets focused at a point F on the x axis By using the concept of optical path length calculate the focal length f Assume f t and consider y to be small 2 Yo y X

An object of height h 3 cm is placed at a distance of 5 cm in front of a convex spherical mirror with focal length of magnitude 10 cm The height of the image is Oh 6 cm Oh 2 cm Oh 1 5 cm Oh 1 5 cm Oh 6 cm

An equi convex thin lens of glass u has focal length in air as 20 cm Now one of its convex face is silvered to make equivalent mirror In case i this equivalent mirror is kept in air and in case ii it is kept in water u Then O Radius of curvature of convex side of lens is 10 cm Focal length of equivalent mirror in both case is same Focal length in case i is 6 cm Focal length in case ii is 8 cm

Figure shows a thin converging lens for which the focal length is 5cm The lens is in front of a concave spherical mirror of radius R 30 cm If the lens and mirror are 20cm apart and an object is placed 15cm to the left of the lens determine the approximate distance of the final image from the lens in cm

Timinished image of an object is to be obtained on a screen 1 0 m away from it This can be achieved by approximately placing A convex mirror of suitable focal length Your Answer A concave mirror of suitable focal length A convex lens of focal length less than 0 25 m Correct Answer A concave lens of suitable focal length

4 a Suppose lens L1 has a focal length of 5 cm This lens is in direct contact with a second lens L2 If an object is placed 5 cm from the lens combination the resulting magnification is seen to be M 10 Find the focal length of the second lens in the combination a 2 63 cm b 0 2 cm c 50 3 cm a Real Upright Unmagnified b Real Inverted Reduced c Virtual Upright Enlarged d Real Inverted Enlarged d 4 54 cm b Characterize the image that is formed when an object is placed 5 cm in front of the lens combination in terms of Real Virtual Upright Inverted Enlarged Unmagnified Reduced and tell why

25 A ray of light travelling in air is incident at angle 0 30 on a long rectangu of a transparent medium The point of incidence is origin O of the coordinate system as shown in the figure 8 X Air The medium has a variable index of refraction y given by 0 25 ky 2 1 2 where k 1 0 m Calculate the equation for trajectory of the ray in the medium b y 4x a x 4y c y 4x d x y 4

A double concave lens has equal radii of curvature of 15 1 cm An object placed 14 2 cm from the lens forms a virtual image 5 29 cm from the lens What is the index of refraction of the lens material O 1 98 O 1 90 O 1 77 O 1 52 1 82

A light ray strikes a homogeneous rectangular block of glass of thickness w at an angle i The ray emerges at point B at an angle i see diagram below a Find i in terms of i and show that the emerging and incident rays are prallel b Find the lateral displacement which is the distance d between the incident and emerging rays in terms of angle i the refractive indices n and n and width w of the block c Use the formula obtained in part b to calculate d

A glass slab of refracctive index 2u is sandwiched between two transparent slabs of refractive indices 2 and 3 u respectively as shown in the figure What should be the minimum angle of incidence i for which light once entered into it will not leave it through the lateral faces Bor air 2 ic incident ray 1 sin sin 1 M 2 py 7 sin 1 5 08 2 2 3 S 2 sin 3 oin 1 u 200 sa

Q 59 A concave spherical surface of radius of curvature 10 cm separates two mediums X and Y of refractive indices 4 3 and 3 2 respectively Centre of curvature of the surface lies in the medium X An object is placed in medium X Will the image be real or virtual

c Wrap up questions Use the simulation to answer each of the questions below Be sure to include your responses in your lab records 1 Can a real image be created using a diverging lens If so how 2 How does the distance of the object from a diverging lens affect the image distance 3 How does the distance of the object from a diverging lens affect the image size 4 How does the distance of the object from a diverging lens affect the image orientation 5 Given the above what would be an appropriate application of a diverging lens

A glass slab is placed between an object 0 and an observer E with its refracting surfaces AB and CD perpendicular to the line OE The refractive index of the glass slab changes with distance y from the face AB as Ho 1 y Thickness of the slab ist Find how much closer compared to original distance the object appears to the observer Consider near normal incidence only 4 D 0

ghtly loose to a wire frame as in figure and the frame is dipped into a soap solution and taken out the frame is completely covered with the film When A is pricked wire frame Thread 1 thread will become concave on seeing from side A 2 thread will become concave on secing from side B 3 thread will become straight 4 thread will remain as it is

v Choose the correct statement a The angle of incidence is greater than the angle of emergence at refracting surface b The angle of incidence is smaller than the angle of refraction at the fir v refracting surface c The angle of incidence is smaller than the angle of refraction at the refracting surface a May b May be 15 c May be 20 d Must be Which of th a Work de b Work c Work d Work

A thin rod of length 10 cm lies along the principal axis of a concave mirror of radius of curvature 20 cm in such a way that the end closer to the pole of mirror is at distance 20 cm away from it The length of the image of the rod will be 1 10 cm 2 5 cm leda muminim 3 8 cm 4 15 cm srW

A 1 cm B 6 cm A 1 2 cm long pin is placed perpendicular to the principal axis of a convex mirror of length focal 12 cm at a distance of 8 cm from it then position and height of image are respectively A 4 8 cm 0 72 cm B 3 4 cm 0 36 cm C 6 4 cm 0 8 cm D 3 2 cm 0 64 cm mirror If the image

Object iii iv V Optical axis Image Question 10 Which of the rays in the diagram are consistent with the formation of the image The image is real Lens V The image is shrunk The image is inverted iv iii ii i 6 22 Consider a converging mirror with a radius of curvature of 1 5 m If an object is placed 2 0 m in front of the mirror which of the following statements about the image formed is are correct 3 pts

A 12 cm B 15 cm C 18 cm A dentist uses a small mirror that gives a magnification of 4 when it is held 0 60 cm from a tooth The radius of curvature of the mirror is A 0 96 cm convex B 0 8 cm concave C 0 96 cm concave D 0 8 cm convex 20 cm If a point of object is placed at a distance

Conceptual Difficulty Medium Concept Included Error Analysis swer A B 60 4m 53s 48 4m 23s 30 Save A light ray is incident on a glass sphere of equation x y 2 a If the ray moves along the line y from left to right in the x y plane from outsi the sphere The angle of deviation suffered by the light ray as the ray comes out of the sphere is the refractive index of glass is 2 Rate this questic SMCQ 3 1 62 39 47 38

y A biconvex thin lens of radius of curvature R is made up of variable refractive index 2 1 d Assume very small aperture 2d R A point object O is placed at a disatnce R 7 5 m on the principal axis from the lens as shown Due to variable refractive index of lens there are infinite number of image on the principal axis These image are spreaded over the length Find the value of in m AY O R P R R d d

A small source of light is mounted inside a cylindrical container of height h The bottom of the container is covered with a mirror Initially the container is empty Then a clear liquid with the index of refraction n is slowly poured into the container The level of liquid H rises steadily reaching the top of the container in time T Let hy be the distance of source of the light from the bottom of the container Consider paraxial ray approximation Consider two cases near normal incidence only Source of light Mirror Case P H hy Light rays from source travel down and then mirror sends them back into a eye above the container Case Q h H h Light rays directly go up refract through water and reach eye above container 1 A The speed of the image of the source in case P during this process is 1 B The speed of the image of the source in case Q during this process is C The speed of the image of the source in case P during this process is DI The speed of the image of the source in case O during this process is hy 1 1

In column I all the objects x 0 shown are real In column II nature of image is mentioned Rays a paraxial consider all the possibilities of nature of images then match column I with column II Column I Column II A B C D object H X object object object If Prism X concave mirror H Convex mirror Plane refracting P Real Q Virtual R Magnified Large S Diminished Small

c 3 8 cm 29 Each quarter of a vessel of depth H is filled of the refractive index n n n n from the bottom respectively The apparent depth of the vessel when looked normally is a H 4 n n n n b H 4 n n n n c n n n n 4H d H 1 4 m 1 d 3 cm 1 1 n4 N N3

34 A ray of light is incident at an angle of 45 on one face of a rectangular glass slab of thickness 10cm and refractive index 3 2 Calculate the lateral shift produced a 0 33 m b 0 45 cm c 0 033 m d 0 045 m Rofrontive index of water and glass are 4 3 3 2 tor is inciden

Example 91 A concave lens of focal length 10 cm is placed on the axis of a concave mirror of 10 cm radius at a distance of 5 cm from the mirror An object is placed so that the light coming from it first passes through the lens then gets reflected from the mirror again passes through the lens to form an inverted image coincident with the object itself Determine the position of the object