Geometrical Optics Questions and Answers

F 30 0 52 A thin convex lens having focal length 20 cm is cut into two parts 1 mm above the principle axis The lower portion is placed with optical centre at origin and upper portion at 90 0 as shown in the figure A point object is placed at 30 0 Find the magnitude of y coordinates in mm of the image Assuming paraxial ray approximation to remain valid 30cm ANSWER 4 0 0 00 59 90cm 90 0

53 A thin plano convex lens of focal length fis split into two halves one of the halves is shifted along the optical axis The separation between object and image plane is 1 8 m The magnification of the image formed by one of the half lenses is 2 Find the focal length of the lens in decimeter 1 decimeter 10 cm ANSWER 1 8m

An object of height 18 cm is kept at a distance of 50 cm in front of a mirror of focal length 25 cm The mirror forms a real image of the object a Identify the type of the mirror b Calculate the distance of the image from the mirror c Find the height of the image

ALLEN 41 An equiconvex thin lens of focal length is cut into two identical pieces alor diameter and pieces are arranged a shown in the given figure The net foc length of the combination is n 1 2 f

ou place an object 15 8 cm in front of a diverging lens which has a focal length with a magnitude of 12 6 cm Determine how far in front of the lens he object should be placed in order to produce an image that is reduced by a factor of 4 45 1 8 X an you write the thin lens equation that gives a relationship between the focal length of a lens the object distance and the image distance an you write the thin lens equation that gives a relationship between the object distance image distance and magnification cm

One face of a biconvex lens of radius R R 30 cm and 1 5 is silvered as shown in the figure The image of a point object placed at a distance 60 cm from the lens on its optic axis is formed at a distance 0

A convex meniscus lens is made from glass with refractive index n 1 52 If the radius of curvature of the convex surface is 20 cm and that of the concave surface is 40 cm then find out the focal length A 129 cm B 94 cm C 80 cm D 113 cm

2 A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of magnitude of focal length 20cm A beam of parallel light falls on the diverging lens The final image formed is 2017 1 real and at a distance of 40cm from the divergent lens 2 real and at a distance of 6 cm from the convergent lens 3 real and at a distance of 40 cm from convergent lens 4 virtual and at a distance of 40cm from convergent lens

A convex lens of focal length 15cm produces virtual image whose size is thrice the size of the object 1 Calculate the object and image distance 2 Marks ii Calculate the height of the object if the height of the image is 6cm 1 Mark iii Explain the properties of the image by drawing the ray diagram 2 Marks

Example 9 8 i If f 0 5 m for a glass lens what is the power of the lens ii The radii of curvature of the faces of a double convex lens are 10 cm and 15 cm Its focal length is 12 cm What is the refractive index of glass iii A convex lens has 20 cm focal length in air What is focal length in water Refractive index of air water 1 33 refractive index for air glass 1 5

Example 4 Suppose while sitting in a parked car you notice a jogger approaching towards you in the side view mirror of R 2 m If the jogger is running at a speed of 5 m s how fast the image of the jogger appear to move when the jogger is a 39 m b 29 m 19 m and d 9 m away

Position of 4th image of mirror M is 1 2 3 15cm M Question Type Single Correct Type 4 69 cm from M 48 cm from M English 78 cm from M 57 cm from M 6cm O M Review

ght Incident normally on one of the faces of a right angled isosceles prism is found to be totally reflected as shown X1 Toucs What is the minimum value of the refractive index of the material of the prism Lage 7314 The Board Examination 1242 When a prism is immersed in water trace the path of the emergent ray for

An object is placed 30 cm from the reflecting surface in front of a block of glass 10 cm thick having its farther side silvered The final image is formed at 23 2 cm behind the silvered face The refractive inde of glass is A 1 41 B 1 46 C 200 132 D 1 61

Question 7 An extended fixed object AB is in contact with a convex mirror focal length Im mounted on a stand as shown Now the mirror is given an initial velocity of 2m s towards right If coefficient of kinetic friction between ground and mirror stand is 0 3 then in m s of the image of point B Take find the magnitude of initial acceleration g 10m s Principal axis

angle u angled triangular prism of refractive index n 2 Light undergoes total internal reflection in the prism at the face PR when a has minimum value of 45 The angle of the prism is P a n R

A small object is moving towards a plane mirror with velocity V 10 m s and the plane mirror is moving with velocity V 5 m s as shown The speed of image is nonim Object 1 2 10m s 3 10 2 m s V 1 45 TTT 2 5 5 m s 4 5 10m s

In a spherical paper weight R 10 cm made of 3 glass of refractive index 2 C 3 2 embedded at a distance 5 cm from its centre What is the apparent position of the object when seen from the opposite side see figure P 1 10 cm behind centre 2 10 cm behind P 3 15 cm behind centre A 5 cm behind P an object is Observer air 1 vieneint

An equiconvex lens of u 1 5 and radius of curvature R 20 cm is placed in front of a convex mirror of radius of curvature 20 cm as shown An object is placed as indicated The possible value of x so that the image coincides with the object is Object 30 cm 1 30 cm 3 90 cm X 2 60 cm 4 50 cm

4 240 360 2 Two mirrorsAB and CD are arranged along two parallel lines The maximum number of images of object O that can be seen by any observer is MAVFUMOTEXANSLATE

13 Assertion When a convex lens is placed on a plane mirror image of a pin object can be obtained coinciding with the pin itself Reasoning The location of the object is the focal length of the lens 14 Assertion There are some phenomena shown by light that ca not be explained by the considerations of

f 43 For a compound microscope of length L the focal length of objective and eye piece are fo and respectively magnification If D 25 cm then approximate for normal adjustment is LD 1 fofe 3 fofe terte to su S 2 4 L D fo fe 1 fofe

As shown in the figure point O is located at a distance 15 cm from the interface of two surfaces Point C denotes the center of curvature of the separating surface Determine the location of the image of point O 1 0 1 50 A B 20 cm 30 cm c 27 cm D 25 cm 15cm R 45cm

A plano convex lens when silvered at its plane surface is equivalent to a concave mirror of focal leng 28 cm When its curved surface is silvered and the plane surface not silvered it is equivalent to concave mirror of focal length 10 cm then the refractive index of the material of the lens is A 9 14 B 14 9 C 17 9 D none of these the radius of curvature of the curved surface of plano convex lens is

A dentist has a small mirror of focal length 16 mm He views the cavity in the tooth of a patient by holding the mirror at a distance of 8 mm from the cavity The magnification is a 1 c 2 72 A light ray from air is incident as shown in figure at one end of a glass fibre refractive index 1 5 60 making an incidence angle of How much time would it take to Air Air 60 1 4979330 Glass b 1 5 d 3 the lateral surface so that it undergoes a total internal reflection km 916 Taverse the straight fibre of length 1 a 3 33 l s c 5 77 l s 73 Pick the correct statement from the following a Primary rainbow is a virtual image and secondary rainbow is a real image b 6 67s d 3 85 s b Primary rainbow is a real image and secondary rainbow image TA COM

A silvered ball of radius r 5 0 cm is so suspended that its centre is h 1 0 m above the floor and so 2 0 m horizontally away from a person of height ho 2 0 m There is also a large plane mirror which stands vertically at some distance from the person If the person sees his image in the ball as small as he sees his image in the plane mirror how far is the plane mirror from the person 450 ho loom Lir

the reflected ray is rotated by an angle of 40 in cloc direction then the mirror was rotated by a 20 in anti clockwise b 40 in anti clockwise direction direction c 20 in clockwise direction d 40 in clockwise direction

A denser medium of refractive index 1 5 has a concave surface of radius of curvature 12 cm An object is situated in the denser medium at a distance of 9 cm from the pole Locate the image due to refraction in air 1 A real image at 8 cm 2 A virtual image at 8 cm 3 A real image at 4 8 cm 4 A virtual image at 4 8 cm

i A ray of light incident on face AB of an equilateral glass prism shows minimum deviation of 30 Calculate the speed of light through the prism ii Find the angle of incidence at face AB so that the emergent ray grazes along the face AC

T 46 In displacement method we use a lens of focal length fand distance between object and screen is 60 cm Possible value for focal length is 1 15 cm 2 30 cm 3 12 cm 4 20 om UITI

0 45 Which one of the following statements is true a An object situated at the principle focus of a concave lens will have its image formed at infinity c C Given www b 60 d 30 b Concave

A ray of light OP passes through a right angled prism as shown in the above diagram a State the angles of incidence at the faces AC and BC b Name the phenomenon which the ray suffers at the face AC A OP 45 45

A glass plate has a thickness r and refractive index The angle of incidence of a ray from air into the plate is equal to the critical angle for glass air intrerface The lateral shift perpendicular distance between incident ray and emergent ray of ray is given by 2 14 1 1 1 3 1 1 2 1 4 t 2 1 1

3 At what distance from a convex mirror of focal length 2 5 m should a boy stand so that his image has a height equal to half the original height The principal axis is perpendicular to the height Solution We have or Also or or m V HBHB 1 1 1 u 1 u U U u u 2 u f 1 u 2 1 2 5 m 1 2 5 m 2 5 m or Thus he should stand at a distance of 2 5 m from the mirror

QLight is incident normally on face AB of a prism as shown in fig A liquid Of refractive index is placed on face AC Of the prism The prism is made of glass of refractive index 312 The prims of for Which total Internal reflection takes place on face AC is Claud 60 30 60 90 B 30 C

In the setup shown above the refractive index of the prism is A horizontal ray is entering at height h and emerges as horizontal ray at height After two TIR as shown Then is given by h sin 0 sin 30 Sr Super60 All A B h Cos 0 cos 30 2 1 fl Space for rough work C 0 D h l 1 2 Page

Problem 2 Monochromatic light of wavelength 5890 is incident from air on water surface What are the wavelength frequency and speed of a reflected and b refracted light Refractive index of water is 1 33

A deviation of 2 is produced in the yellow ray when prism of crown and flint glass are achromatically combined Taking dispersive powers of crown and flint glass as 0 02 and 0 03 respectively and refractive index for yellow light for these glasses are 1 5 and 1 6 in degree respectively The refracting angles for crown glass prism will be Round off to the Nearest Integer

There is a prism with retractive index equal to V3 and the refracting angle equal to 30 One of the refracting surfaces of the prism is polished A beam of monochromatic light will retrace its path if its angle of incidence over the refracting surface of the prism is Question Type Single Correct Type 1 0 2 30 3 45 60

3 In a particular scene of a science fiction movie a UFO is flying horizontally at a very high altitude with a speed u that is n 1 times of speed c of light The UFO is emitting sharp light pulses at regular and very small intervals Find the speed of the UFO recorded by an observer on the ground at point O when the UFO appears at an angle with the vertical Ignore relativistic corrections A UFO un identified flying object is believed to be a space ships used by aliens

43 A thin prism has different medium on its either side A light ray is incident almost normally on the first face What is the angle of deviation if all the angles are very small H1 14 AAJ KA TOPPER 1 1 1 4 4 1 4 2 1 1 4 A 1 3 1 1 4 A 1 4 A 4 None of these

Define the distance at which the person can read the book without glasses if his glasses power is 3 5 diopters Select one O 50 cm O 28 9 cm 02m O 26 9 cm

respectively A beaker contains Water and Benzene of refractive indices one above the other If depth of each is 12 cm apparent depth of the bottom of 3 2 the beaker is 1 16 cm A layer of benzene u 2 17 cm 1 3 18 cm 4 and 3 4 19 cm 1 33 1 cm deep

When focused on a distant object the focal length of your eye s combined cornea and lens is f To focus on a nearby object the focal length of your eye s lens must A Increase B Decrease Q5 A farsighted boy has a near point at 2 3 m and requires contact lenses to correct his vision to the normal near point What is the correct choice of lens power for the contact lenses A 3 6 diopters B 1 8 diopters C 0 28 diopters D 3 6 diopters

The base of a tank is horizontal glass plate 8 cm thick u 1 6 Above this i layer of liquid of thickness 4 5 cm 1 5 and upon this floats a layer of wa 12 cm thick Looking from the above the apparent position of the spot 3 the bottom of the tank is 1 17 cm 2 19 cm 3 21 cm 4 35 cm

A ray of light enters a rectangular glass of slab of refractive index 3 at an ang of incidence 600 It travels a distance of 5 cm inside the slab and emerges out the slab The perpendicular distance between the incident and emergent ray is 4 5 3 cm cm 52 S 3 5 2 cm

A converging beam of rays is incident on a divergin lens Having passed through the lens the ra intersect at a point 15 cm from the lens on th opposite side If the lens is removed the point whe the rays meet will move 5 cm closer to the ler The focal length of the lens is 1 30 cm AIPMT Mains 201 X 2 5 cm

A bird looking down vertically into a pond from 12 cm above the surface sees a fish apparently 18 cm below the surface What is the apparent height of bird as seen by fish w 4 3 1 12 cm 2 18 cm 3 16 cm 4 40 cm

The refractive index of glass is The time taken by a monochromatic light rays 2 to travel a distance d in air is 4s The time taken by the light ray to travel the same distance in glass is 1 4s 2 6s 3 8 3 S 4 3s

In the diagram an object is placed at distance 20 cm from pole In this condition object and image coincide Radius of curvature of mirror is 25 cm Refractive index of liquid is of 1 413 15 cm 2 3 2 5 cm