Geometrical Optics Questions and Answers

26 A ray of light suffers a minimum deviation when incident on an equilateral prism of refractive index 2 The angle of incidence is a 30 b 45 c 60 2016 d 50

Angle of a prism is 30 and its one surface is silvered Light rays falling at an angle of incidence 60 on the first surface returns back through the same path after suffering reflection at the silver surface The refractive index of the prism is 1 1 5 3 2 2 3 4 none of these

5 magnit 4 Real inverted and diminished In compound microscope magnification is 95 and the distance of object from objective lens is 3 cm and focal length of objective is 2 cm What is the magnification of eyepiece when final image is formed at least distance of distinct vision 2 46 5 4 46 2 1 47 5 3 47 2

0 4 h Consider the setup shown in the figure which uses a right angled prism to transmit a horizontal incident ray This device is known as anamorphic de magnifier During its passage through the prism the ray experiences total internal reflection TIR twice and then exits as shown in the figure The prism is made from a glass of refractive index 12 If the emerging ray propagates horizontally which of the following is a correct expression for refractive index u a c sin sin 30 cose sin 30 b d sin cos 30 Cos cos 30

a 13 Range of values of tip angle for the device to work as anamorphic de magnifier is 1 1 cos sin hy Consider the setup shown in the figure which uses a right angled prism to transmit a horizontal incident ray This device is known as anamorphic de magnifier During its passage through the prism the ray experiences total internal reflection TIR twice and then exits as shown in the figure The prism is made from a glass of refractive index u 0 sin in l 11 2 b sin 1 0 co 1 0 Cos 1 COS COS d 1 F 43 1

a lens of focal length fis divided into two equal parts and both pieces are put in contact as shown in fig The resultant fo cal lengths of the combinations are ADD DD 1 0 f co 2 f f 0 3 2 f f 0 4 f f 2 00

36 A thin convex lens of focal length 12 cm is placed 6 cm apart from a thin concave lens of focal length 15 cm Find out position of both the principal points A 15 cm 15 cm B 6 cm 6 cm C 4 cm 5 cm D 8 cm 10cm

28 The velocity of image w r t ground in the below figure is 5 m s 20 cm f 30 cm Mirror is at rest given velocity w r t ground 1 45 m s towards the mirror 2 45 m s away from the mirror 3 60 m s towards the mirror

Height of water that would be filled in a container of height 21 cm so that it appears half filled to the observer when viewed from the top of container is M 4 3 1 8 cm 3 12 cm 2 10 5 cm 4 14 cm

SINGLE AND DOUBLE VALUE INTEGER TYPE A fluorescent lamp of length 1 m is placed horizontally at a depth of 1 2 m below a ceiling A plane mirror of length 0 6 m is placed below the lamp parallel to and symmetric to the lamp at a distance 2 4 m from it as shown in figure Find the length in meters distance between the extreme points of the visible region along x axis of the reflected patch of light on the ceiling 11 2m 1m 0 6m 2 4m X

54 A light ray I is incident on a plane mirror M The mirror is rotated in the direction as shown in the figure by an arrow at frequency 9 1 rps M The light reflected by the mirror is received on the wall W at a distance 10 m from the axis of rotation when the angle of incidence becomes 37 the speed of the spot a point on the wall is a 10 m s c 500 m s 37 b 1000 m s d 20 m s 10m W

Example 8 9 A rod AB rests with the end A on rough horizontal ground and the end B against a smooth vertical wall The rod is uniform and of weight If the rod is in equilibrium in the position shown in figure Find a frictional force at A b normal reaction at A c normal reaction at R

6 The graph between u and u for a convex mirror is a c f U I U b d u

A point object is placed on principal axis of a concave mirror of radius of curvature 20 cm at a distance 31 cm from poll of the mirror A glass slab of thikness 3 cm and refractive index 1 5 is placed between object and mirror as shown in the figure Find the distance in cm of final image formed by the system from the mirror R 20cm bir 3 2 3am 31cm

7 A beam of light consisting of red green and blue colours is incident on the surface of a liquid as shown in figure The R I of liquid for red green and blue colours are 1 9 2 1 and 2 2 respectively then 1 Red colour will separate from the beam 2 Blue colour will separate from the beam 3 Separation of all the component colour wil 4 Occur 30 All of thos

A small air bubble is inside a glass cube of side 15 cm When seeing from the top face the bubble appears at a distance of 5 cm and if seen from the opposite face it appears at 7 cm Refractive index of glass is 1 3 5 4 5 2 4 3253

95 A person can see clearly only upto a distance of 25 cm He wants to read a book placed at a distance of 50 cm What kind of lens does he require for his spectacles and what must be its power 1 Concave 1 0 D 3 Concave 2 0 D 2 Convex 1 5 D V Convex 2 0 D Z NOCE02 GET PHY ENGMODULE 06101 RAY C

12 The time taken by a monochromatic light to travel a certain distance in air in 9 x 10 6 seconds The time take by the light ray to travel the same distance in water of refractive index is 4 1 12 s 27 4 3 4 0 4 m s 2 12 s 27 2 4 us

14 A transparent cube contains a small air bubble Its apparent distance is 2 cm when seen through one face and 5 cm when seen through other face If the refractive index of the material of the cube is 1 5 the real length of the edge of cube must be 1 7 cm 2 7 5 cm 14 3 10 5 cm 4 cm 3 anal Services Limited Regd Office Aakash Tower 8 Pusa Road New Delhi 110005 Ph 011 47623

Q19 Size of image of an object by a mirror having a focal length of 20 cm is observed to be reduced to 1 3rd of its size At what distance the object has been placed from the mirror What is the nature of the image and the mirror Draw ray diagram to show image formation for the above situation

Relation between critical angle refractive index if second medium is air

Answer Q 8 Q 9 and Q 10 by appropriately matching the information given in the three columns of the following table 1 II III IV For convex lens focus distance is given by Relation f 1 1 Then lens material and R R are radii of curvature of curved part Power of lens is defined is P f consider following three column geo Culumn 1 Which of the following options is correct combination A 1 B 1 D II ii P Which of the following options is correct combination A II i R G 0 D B II ii S D D ii S Q 10 1 1 R R2 Column 2 i 2P ii P 2 where is refrective index of iii 3P iv P P A III iv Q B III iii S C II iv Q D IV iv P Column 3 Q f 2f R f 2 S f 3 Which of the following options is correct combination

4 T 2C 17 The apparent depth of water in cylindrical water tank of diameter 2R cm is reducing at the rate of x cm min when water is being drained out at a constant rate The amount of water drained in cc minute is n refractive index of air n refractive index of water 1 X R n 772 3 2TRn 1 2 XTR n n 4 R2X

2 A beam of light composed of red and green ray is incident obliquely at a point on the face of rectangular glass slab When coming out on the opposite parallel face the red and green ray emerge from 1 Two points propagating in two different non parallel directions 2 Two points propagating in two parallel directions 3 One point propagating in two different directions 4 One point propagating in the same directions

Two plane mirrors are inclined at an angl of 75 to each other Find the total numbe of images formed When an object placed as shown in figure 45 30 45 0

An astronomical telescope consists of two convex lenses If focal length of objective is 1 0m and angular magnification is 10 find the length of the tube between objective and eyepiece such that final image is formed at infinity 1 1 2m 3 1 4m 2 1 1m 4 1 5m of 15cm from a C

1 A prism of material refractive index u has refracting angle A For which of the following conditions there will be no emergent light whatever may be the angle of incidence 1 U sin 1 A 2 3 COSA 11 2 sinA A

Q 5 Find the focal length of a convex mirror whose radius of curvature is 32 cm

17 X Class Focal length of a spherical mirror is f and object placed at unit distance gives you magnification as m Then which of following is correct A D 1 m 18 Let f is the focal length of a concave mirror then its ratio with the distance P of an object placed from the principal focus in front of the mirror is 1 m 1 1 1 P A 1 m tes f v f A m B f 1 m B f P m 1 m 1 Which of the following has high field view of object A plane mirror B concave mirror B m C f C f f u 1 P C convex mirror D we can t decide The magnification m image distance v focal length f and object distance u of a spherical mirror can be related as 1 m C m m V D u D all the above X Class

A green light is incident from the water to the air water interface at the critical angle 0 Select the correct JEE Mains 2014 statement a The entire spectrum of visible light will come out of the water at an angle of 90 to the normal b The spectrum of visible light whose frequency is less than that of green light will come out of the air medium c The spectrum of visible light whose frequency is more than that of green light will come out to the air medium d The entire spectrum of visible light will come out of the water at various angles to the normal

0 The magnification m image distance v focal length f and object distance u of a spherical mirror can be related as A m f v f B m f f u C m u D all the above

A telescope has an objective lens of focal length 200 cm and an eye piece with focal length 2cm If this telescope is used to see a 50 meter tall building at a distance of 2km what is the height of the image of the building formed by the objective lens 1 5 cm 3 1 cm 2 10 cm 4 2 cm

An air bubble in glass 1 5 is situated at a distance of 3 cm from a spherical surface of diameter 10 cm as shown in figure At what distance from the surface will the bubble appear if the surface is a convex b concave p 1 5 C OF X A 3cm 5cm H 1 P u 1 5 O 3cm P 1 5cm Same 10m

46 A rod of glass m 1 5 and of square cross section is bent into the shape shown in the figure A parallel beam of light falls o plane flat surface A as shown in the figure If d is the width of a side and R is the radius of circular arc then for what maximum light entering the glass slab value of d n R 100 through surface Aemerges from the glass through B The value of n is d A B

A plane mirror makes an between the mirror and the reflected ray Figure shows the plane top view of a cubical room with the wall CD as a plane mirre of the room is 3 metres in length A camera P is placed at the mid point of the wall AB At what distance should the camera be focused photograph the image of an object placed at A

1 1 4 3 2 2 A plane mirror is placed horizontally on level ground at a distance of 60 m from the foot of a tower from the top of tower falling just on the edge of the mirror suffers a deviation of 90 The height is

There are three optical media 1 2 and 3 with their refractive indices u H2 3 Then A when a ray of light travels from 3 to 1 no TIR will take place B critical angle between 1 and 2 in less then critical angle between 1 3 C critical angle between 1 2 in more than critical angle between 1 3 D Chances of TIR are more when ray of light travels from 1 to 3 as compared to the case when it travels from 1 to 2

the position magnification and natur A motor car is fitted with a rear view mirror of focal length 20 cm A second rotor car 2 m broad and 21 6 m high is 6 m away from first car Find the position of second car as seen in the mirror of the first car A virtual image three times the size of the object is obtained with a concave mirror of radius of curvature

6 A ray of light falls on the surface of a spherica glass sphere making an angle a with the norma and is refracted in the medium at an angle The angle of deviation of emergent ray from the direction of incident ray is 2 2 B 1 B B 2 3 4

A plane mirror of length 8 cm is with speed 3 m s towards a wall in situation as shown in figure A source of light S gives narrow and parallel light on to the mirror then the speed of light spot formed on the wall is A 8 m sec S Source of light 3m s Wall K4 8cm B 6 m sec

0 8 9 Answer Q 8 Q 9 and Q 10 by appropriately matching the information given in following table For convex lens focus distance is given by Relation f 1 1 1 lens material and R R are radii of curvature of curved part Power of lens is defined is P Then f consider following three column Culumn 1 II III IV or Which of the following options is correct combination A 1 ii Q B I ii P C II iii Q D II ii P Which of the following options is correct combination A II i R C 1 iv Q 1 1 D R R B II ii S D 1 ii S Q 10 Column 2 i 2P ii P 2 where u is refrective index of iii 3P iv P P A III iv Q B III iii S C II iv Q D IV iv P Column 3 Q f 2f R f 2 S f 3 Which of the following options is correct combination

refracting acute angle of biprism is The a 179 b 1 c 1 2 d 90

The power of spectacles lens required for a is 5 dioptre when separation between spe and eye is 2 cm What will be the power of lens required by him 1 5 25 D 3 32 D 2 4 54 D

3 A light is travelling from air into a medium Velocity of light in a medium is reduced to 0 75 times the velocity in air Assume that angle of incidence i is very small the deviation of the ray is MH CET 20151 a i c 1 1 2 F b d 113 314 3i

An optical fibre consists of core of n surrounded by a cladding of n2 ni A beam of light enters from air at an angle a with axis of fibre The highest a for which ray can be travelled through fibre is 2 2 a cos n n 2 b sin n n c tan n n 2 2 d sec n n O n M

2 Two mirrors are inclined at an angle 0 as shown in the figure Light ray is incident parallel to one of the mirrors Light will start retracing its path after third reflection if a 0 45 c 8 60 0 b 0 30 d all three

An isoceles glass prism stands with its horizontal base in water as shown in the figure An incident ray of light above and parallel to the liquid surface and perpendicular to the prism s axis is internally reflected at the glass liquid interface and subsequently re emerges into the air Refractive index of glass is and liquid is then which g relation holds good 0 0 Liquid a cos 0 1 2 1 b g cos 0 c cos e

0 Question 3 O 60 O 34 In the figure the second angle of incidence Zis 24 190 r O 19 60 90 1 Take the refractive index of the prism material as 1 6 and i 45

A concave mirror of focal length f is placed at a distance of d from a convex lens of focal length f A beam of light coming from infinity and falling on this convex lens concave mirror combination returns to infinity The distance d must equal 2 2f f 4 f f 1 2f f2 13 1 f27

A compound microscope having f 7 mm f 20 mm and distance between the lenses is 20 cm If image is formed at least distance of distinct vision then magnifying magnifying power 337 3 220 2 400 4 120