Geometrical Optics Questions and Answers

An object is moving along the principal axis of a convex lens of focal length 20 cm with a constant velocity of 2ms 1 When then the object is at a distance of the 40 cm from the lens the velocity of the image is A 2ms 1 B 3 1ms 1 Oc 3ms 1

If the critical angle for total internal reflection from a medium to vacuum is 30 The velocity of light in the medium is O 3 108 m s O 1 5 x 108 m s O 6 108 m s O 3x108 m s

A point source of light is kept at a depth h in water having refractive index 4 3 The radius of circle at the surface of water through which light emitted is 3h 37 h 3 3h 7

46 An object is placed at a distance x from a convex lens The power of the lens required to have an image real n times magnified is 1 n 1 2 n 1 3 f f fay nx n 4 nx

When a small lamp is held 1 5m above the surface of water in a tank its image formed by reflection at the surface appears to coincide with the image of the bottom of the tank u of water 4 3 The depth of the tank is

A convex lens of focal length 40 cm is in contact with concave lens of focal length 25 cm The power of combination is O 1 5 D O 6 5 D 6 5 D

One surface of prism with prism angle 30 and refractive index of material 2 is silvered At what angle a ray of light incident on the prism so that after reflection from silvered surface light ray retraces the path 30 60 45 90

The focal length of the objective of an astronomical telescope is 1 0 m If the magnifying power of telescope is 20 then the length of telescope for relaxed eye is 85 cm 95 cm 105 cm 115 cm

Does a spherical lenses have 2 p oles Like in a mirror we say the p oint where the principal axis touc hes the reflecting surface as pole so in lenses do we have 2 poles since the principal axis crosses th e lens in 2 points

ABC is a right angled prism of transparent material of refractive index such that ZB is smaller than ZA as shown in figure A ray of light incident mormally on the face AB emerges parallel to the ncident ray after two internal reflections then the minimum value of u is 1 3 1 sin A sin A C 2 sin B 4 sin 6 sin B

In YDSE when a glass plate of refractive index 1 5 of thickness tis introduced in path of one interfering beam wavelength X the intensity at position where the central maxima occurred previously remains unchanged The minimum thickness of glass plate is Ox 21 N W

B The height of mai intage this An object is placed at a certain distance from a screen A convex lens of focal length 40 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 10 17 cm Find the distance of the object from the screen 20 pm If a glass slah

48 For the given incident ray as shown in figure the condition of total internal reflection of this ray the required refractive index of prism will be 1 3 1 2 2 2 1 2 45 incident ray 3 312 4 76 V6

A glass slab of dimensions 6 x 4 cm is placed such a way that length and breadth are parallel to x axis and y axis respectively as shown in figure If ejected ray from slab is represented by equation y x then Refractive index of medium of glass 1 5 y A SRAM ATHE A y x is equation of incident ray B The incident ray must fall on slab on the side of ve y axis 1 C Lateral shift of the incident light ray is 4 4 1 2 7 7 D The slab is shifted parallel to its length by small length d then final ray will be y x d

m is al of between these two colours when they emerge ou 1 659 respectively then the angular separation of the prism is 1 0 9 3 1 8 The focal length of a thin convex lens for red and blue rays are 100 cm and 96 8 cm respectively The dispersive power of the material of the lens is 2 0 09 4 1 2 1 0 0325 2 0 825 3 0 968 4 0 98 The refractive indices of the material of a lens for violet yellow and red colours of light are 1 66 1 64 nd 16 respectively The mean focal length of the

statement s A ray is incident from the other medium to this medium 0 1 2 are positive H y y Ho x z plane A Ray will definitely return in the medium of refractive index 0 0 any B Ray will never return in the medium of refractive index for value of 1 2 C If ray crosses a particular y then it will never return to medium having refractive index 0

94 Identify the device used as spherical mirror or le Previo in the following cases when the image formed virtual and erect in each case A Object is placed between device and its focu image is enlarged and behind it B Object placed between focus and device imag formed is enlarged and on the same side that of object A 1 Convex lens 2 Convex mirror 3 Concave mirror 4 Concave mirror B 98 Concave mirror Convex lens Convex lens Concave lens Haryana Stage l 2015 1 in of red a

The angle of deviation 8 vs angle of incidence i is plotted for a prism Pick up the incorrect statements 8 65 60 60 O The angle of prism is 60 70 For deviation to be 65 the angle of incidence The refractive index of the prism it O The curve of vs i is parabolic

A ray of light strikes a 90 triangular glass prism at an angle of incidence 0i Determine the refractive index n of the prism as a function of ei if on the opposite face of the prism the light beam remains parallel to the interface The prism is surrounded by air Can you explain me step by step please

Angle of prism is A and its one surface is silvered Light rays falling at an angle of incidence 2A on first surface return back through the same path after suffering reflection at second silvered surface Refractive index of the material of prism is 1 2 sin A 2 2 cos A 4 tanA 1 3 COSA 2 111

A thin lens has focal length fand its aperture has diameter d It forms an image of intensity Now the central part of the aperture upto diameter d 2 is blocked by an opaque paper The focal length and image intensity will change to O f 2 1 2 f 1 4 34 112

A point source of light is kept at a depth hin water having refractive index 4 3 The radius of circle at the surface of water through which light emitted is 3h 37 h 3 3h 7

A convex lens makes a real image 4 cm long on a screen When the lens is shifted to a new position without disturbing the object we again get a real image on the screen which is 16 cm long The size of object will be O 1 4 cm 8 cm 12 cm 20 cm

O 1 5 D A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm The power of combination is 6 5 D hr 6 5 D min

A concave mirror of focal length f in air is immersed in water 4 3 The focal length of mirror in water will be Of 4 f 3 3 f 4

A paperweight is made of a solid glass hemisphere of index of refraction 1 53 The radius of the circular cross section is 4 0 cm The hemisphere is placed on its flat surface with the center directly over a 1 5 mm long line drawn on a sheet of paper What length of line is seen by someone looking vertically down on the hemisphere mm

BE 3 6 cm 4 12 cm A convex lens forms a real image of a point object at a distance of 50 cm from the convex lens A concave lens is placed 10 cm behind the convex lens on the image side On placing a plane mirror on the image side and facing the concave tens it is observed that the final image now coincides with the object itself The focal length of the concave lens is 1 50 cm 2 20 cm 3 40 cm I 25 cm

White light is incident normally on a glass slab Inside the glass slab KCET 2012 a Red light travels faster than other colours b Violet light travels faster than other colours c Yellow light travels faster than other colours d All colours travel with the same speed

along the convex side Then the distance in cm of the image is 1 20 2 30 4 12 3 40 Two thin similar convex glass pieces are joined together front to front with its rear portion silvered such that a sharp image is formed 20 cm from the mirror When the air between the glass pieces is replaced by water u 4 3 then the image formed from the mirror is at a distance of 50 d Angle of deviation 1 47 3 45

er ne S S o 4 sin Refraction at Spherical Surfaces A point object is situated at a distance of 36 cm from the centre of the sphere of radius 12 cm and refractive index 1 5 Locate the position of the image due to refraction through sphere 1 24 cm from the surface 2 36 cm from the centre 3 24 cm from the centre 4 Both 1 2 New Delhi 110005 Ph 011 47623456

A coin is placed at the bottom of a tank which is filled by two liquid layers as shown The apparent depth of coin from top of surface for normal viewing is 06 cm O 13 cm O 5 cm O 18 cm 12 cm 6 cm

If the focal length of the lens is 20 cm what is the distance of the image from the lens in the following figure 1 5 5 cm 3 12 0 cm 12 cm 2 7 5 cm 4 20 0 cm D

An object O is placed at a distance x from the focus of a convex lons and its imago I is formed at a distance x from the other focus as shown in the figuro The distanco x x satisfy the relation 3 3 X X 2 faxx 1 x x 21 x x 21 X Os 14

11 Problem 6 Fiber optics are an important part of our modern internet In these fibers two different glasses are used to confine the light by total internal reflection at the critical angle for the interface between the core ncore 1484 and the cladding cladding 1459 0 n COFE Part a Numerically what is the largest angle in degrees a ray will make with respect to the interface of the fiber Omar and still experience internal reflection

3 A converging beam of rays is incident on a diverging lens Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side If the lens is removed the point where the rays meet will move 5 cm closer to the lens The focal length of the lens is a 5 cm c 20 cm b 10 cm d 30 cm 14 Three charges each q are placed at the corners of an isosceles triangle ABC of sides CAMERA BC and AC 2a D and E are the mid points solucion A F2021 08 15 13

25 A vessel of depth d filled with a liquid o refractive index u up to half its depth and the remaining space is filled with a liquid of refractiv index The apparent depth while seeing normal to the free surface of the liquid is 2 d 1 1 9 H4 1 d 3 d 2 1 1 d 4 14 M

Sunbeam makes an angle 0 40 with the surface of the Earth At what angle to the horizontal shou place a flat mirror so that a ray of sunlight after reflection falls on the bottom of a deep well 1 40 2 50 3 80 4 65

3 D 3 1 A ball is projected from top of the table with initial speed u at an angle of inclination 0 motion of image of ball w r t ball u 1 Must be projectile 2 Must be straight line and vertical 3 Must be straight line and horizontal

Digital movie projectors work on the principle of 1 Reflection from micromirrors 2 Refraction from thin lenses 3 Dispersion from thin prisms ibre

Illustration 11 The bottom of a containers made of glass 4 cm thick u 1 5 The container contains two immiscible liquids A and B upto depths of 6 cm and 6 cm respectively What is the shift of the a scratch on outer surface of the bottom of the glass slab when viewed through the container Refractive indices of A and B are 1 4 and 1 3 respectively

3 2 4 Infinite A person 1 6 m tall is standing at the centre between two walls three metre high What is the minimum size of a plane mirror fixed on the wall in front of him if he is to see the full height of the wall behind him 1 0 8 m 3 1 5 m 2 1 m 4 2 3 m D Jona 13

4 8 mm Light enters at an angle of incidence in a transparent rod of refractive index For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of angle of incidence 1 n 2 3 n 1 1 2 n 1 4 n 1 3

1x A ray of light travels from an optically denser to a rarer medium The critical angle for the media is C The maximum possible deviation of the ray will be 1 20 3 C I 2 4 2C

A light ray is moving from denser refractive index to air If the angle of incidence is half the angle of refraction find out the angle of refraction

How much water should be filled in a container of height 21cm so that appears half filled to the observer when viewed from the top of the container 4 3 8 0 cm 10 5 cm 12 0 cm 14 0 cm

the vertical displacement h of the incident ray from the principal axis as shown in figure a The tical displacement of light rays parallel to the axis of a lens is measured as a function of of the lens for paraxial rays is 10 K cm then what is K 5 data is plotted in figure b The distance D from the lens to the screen is 1 0 m If the focal length Screen h lens Figure a In 2 0 2 2 0 h cm Figure b 1 1 2

7 Which of the following ray diagram is correct for the ray of light incident on a lens shown in FX C d Fig D Fig C a Fig A b Fig B F F F Fig A Fig B A child is standing in front of a magic mirror Sho of F F Fig C F F X Class Fig D 0 3 V

A transparent sphere of radius R 2 0 m has mirrored surface on its right half as shown in figure 1 d 2 0 2 1 9 A light ray travelling in air is incident on the left side of the sphere The incident light ray 1 exiting light ray 2 are Parallel separated by distance d 2 0 m Then find the refractive Index of the material here sin 15 0 26 Round off the answer to two significant digits

Signals in form of light pulses are fed at one end of an optical fibre of circular cross section of radius r All the rays from the source lie within a cone of half angle 0 measured from the axis of the optical fibre The refractive index of the material of the fibre is u A light pulse lasts for a duration rand two pulses are separated by a time interval At from each other What can be the maximum length of the fibre so that the output pulses are still distinguishable Ans Le cat seco 1 S T At Light Pulses

The refractive index of a liquid depends on the y coordinate as n no y 1 If a ray of light is incident from air n 1 at origin at a 3 in medium ngle 45 with the y axis then find the slope of the tangent on the path of the light ray when y 0 0 45 O 1 8n 1 16 1 32 1 X