Geometrical Optics Questions and Answers

1 A point object is placed at a distance of 30 cm from a convex mirror of focal length 30 cm The image will form at A infinity B pole C focus R 15 cm behind the mirror

A compound microscope has an eye piece of focal length 10 cm and an objective of focal length 4 cm Find the magnifica tion if an object is kept at a distance of 5 cm from the objec tive so that the final image is formed at the least distance of distinct vision 25 cm

over a a point 0 V m opper nsions lectric Q 14 Two media I and II are separated by a plane surface having speeds of light 2 108 m s and 2 4 x108 m s respectively What is the critical angle for a ray going from I medium to II 1 sin 3 sin 2 5 12 2 sin 4 sin 5 6 2

In a compound microscope the magnified virtual image is formed at a distance of 25 cm from the eye piece The focal length of its objective lens is 1 cm If the magnification is 100 and the tube length of the microscope is 20 cm then the focal length of the eye piece lens in cm is

An equiconvex lens is made of material which has a refrac tive index of 1 6 for blue light and 1 5 for red light Its focal length for red light is 0 20 m The ratio of focal length for red light to focal length for blue light is 0 01N Find the value of N

A convex lens of focal length f and dispersive power w is combined with a concave lens of focal length f2 and dispersive power 02 is such a way that an achromatic doublet of focal length 40 cm is obtained If respectively 40 3 1 2 20 3 40 3 4 20 20 40 3 20 40 2 W2 3 then f and f2 in cm are

A ray of light of intensity I is incident on a parallel glass slab at a point A as shown in fig It undergoes partial reflection and refraction At each reflection 25 of incident energy is reflected The rays AB and A B undergo interference The ratio Imax Imin is B A B C 4 1 8 1 7 1 A B

Q 11 Two plane mirrors are parallel to each other and spaced 20 cm apart An object is kept in between them at 15 cm from A Out of the following at which point image is not formed in mirror A distance measured from mirror A 1 15 cm 3 45 cm 2 25 cm 4 55 cm

5 Monochromatic light is incident on a glass prism of angle A If the refractive index of the material of the prism is a ray incident at an angle 0 on the face AB would get transmitted through the face AC of the prism provided a 0 cosusin A sin 2 b 0 cos usin A sin7 c sinusin A sin d 0 sin usin A sin OI B C

5 A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm If a 50 m tall tower at a distance of 10 km is observed through this telescope in nor mal setting the angle formed by the image of the tower is 0 Then is close to a 1 c 3 b 15 d 9

from them Object e Mirror c Image ages Name of the mirror a b d f 3 2 Which mirror among the above can be used to form the image

combination is in column II are arranged parallel to each other as shown in column I and the number Column II Column I 1 1 LETJ B wwwwwwwm 30 2a 2x 30 p 2 q 3 r 4 s

A converging lens of power 2 D is placed in contact with another lens of power 1 D The combination will behave as A converging lens of focal length 100 cm O A converging lens of focal length 50 cm A diverging lens of focal length 100 cm A diverging lens of focal length 20 cm

A ray of light passing through equilateral triangular glass prism from air undergoes minimum deviation when angle of incidence is of angle of prism What 3 4 is refractive index of the prism O 2 1 61

An isosceles right angled glass prism is immersed in water The refractive indices of 4 3 3 glass and water relative to air are and respectively If a ray of light is incident normally on the shorter face of the prism inside water the angle in degree of deviation it will suffer as it comes out of the prism will be

For the combination of one prism and 2 lenses shown Find the size in cm of final image when the object whose length is 1 cm is located as shown in figure 45 6 cm n 1 5 45 6 cm 10 cm f 20 cm 5 cm f 10 cm

In a given set up a compound microscope is forming the image of an object placed at a distance x from its objective at infinity If the focal lengths of its objective and eyepiece are 5 cm and 20 cm respectively and tube length is 50 cm then x equals O 6 cm 0 7 cm O 8 cm O 5 5 cm

Two observers A B are observing a fish in water u 4 3 Observer A is observing directly but observer B is observing through a lens of focal length 20 cm Given diagram shows the distance at particular instant At this instant IEEEEEEEE A B C D 40cm A be B 20 m s P f 20cm cm from interface 30cm 4 3 Distance of image as observed by A will 160 3 1 Distance of image as observed by A will be 30 cm from interface Velocity of image as observed by A will be 15 m s towards interface Observer B will observe the final image of fish at a distance of 30 cm from lens

A bi convex thin lens of glass focal length in air is 20 cm Now one of its convex face is silvered to make equivalen mirror In case i this equivalent mirror is kep in air and in case ii it is kept in wate 4 3 Then A B ha Radius of curvature of convex side of lens is 10 cm Focal length of equivalent mirror in both case is same C Focal length in case i is 5 cm D Focal length in case ii is 8 cm

concave mirror forms the image of an object kept at 15 cm from its pole twice in size and real Where should the object be kept so that a virtual mage of twice the size of object is formed O 10 cm from pole O 5 cm from pole O3 cm from pole O 8 cm from pole

A concave mirror is kept as shown in figure Its principal axis coincides with the x axis A real object is moving towards the pole of the mirror starting from the o In which region image will never form P Question Type Single Correct Type 1 Between o and C 2 Between C and F 3 Between F and P X 4 Between P and o

A ray of light will not come out of a prism prism angle A for any value of angel of incidence The refractive index of material of prism is Which of he following relation satisfy the above condition O T sin A

A ray of light is incident at an angle of incidence 0 as shown in fig If the angle between the two plane mirror is 90 then for what value of 0 the reflected ray from the 2 nd plane mirror becomes parallel to the incident ray 30 45 60 All of these

A ray of light is incident at the glass water interface at an angle i such that it emerges finally parallel to the surface of water The refractive index of water is increased by adding some impurity The angle of incidence in glass will Air increase water 2 decrease Glass Question Type Single Correct Type 1 r 3 remains same w 4 3 C

The dispersive powers of glasses of lenses used in an achromatic converging pair are in the ratio of 5 3 If focal length of concave len 15 cm then nature and focal length of other lens will be O Convex 9 cm O Concave 3 cm O Concave 12 cm O Concave 9 cm

On a plane mirror a transparent beaker is kept having water upto depth of 8 cm An 4 3 object is kept at a height of 10 cm above water surface How much distance behind the mirror is the image of the object formed 1 16 cm 2 14 cm 3 12 cm 4 18 cm

44 A person is looking at the image of his face in a mirror by holding it close to his face The image is virtual When he moves the mirror away from his face the image is inverted What type of mirror is he using Convex mirror estion pape 2 Combination of mirror and lens 3 Plane mirror

An observer can see through a pin hole the top end of a thin rod of height h placed as shown in the figure The beaker height is 3h and its radius h When the beaker is filled with a liquid up to a height 2h he can see the lower end of the rod Then if the refractive index of the liquid is n 2 find n 3h h

A convex lens forms the image of an object of same magnification when the object is placed at 10 cm and 20 cm from the lens The focal length of the lens is 1 5 cm 3 25 cm 2 15 cm 4 30 cm

45 A plano convex lens when silvered on the plane side behaves like a concave mirror of focal length 30 cm However when silvered on the convex side it behaves like a concave mirror of focal length 10 cm Then the refractive index of the lens is 2 2 0 4 1 5 1 1 0 3 3 0 ah Work

3 180 3A 4 180 3A 34 Rays from a lens are converging toward a point P as shown in figure How much thick glass plate having refractive index 1 8 must be located between the lens and point P so that the image will be formed at P 1 5 cm 3 0 9 cm Glass plate 2 2 4 cm 4 1 6 cm PP 0 4 cm

33 The refracting angle of a prism is A and refractive index of the material of prism is cot A 2 The angle of minimum deviation will be 2 180 2A 4 180 3A 1 90 3A 3 180 3A

3 240 nm 4 820 nm 29 A plane wavefront AB is incident on a concave mirror as shown in figure Then the wavefront just after reflection is 1 B 3 2 30 In a Young s double slit experiment 50 fringes are 4 None of these

An observer can see through a small hole on the side of a jar radius 15 cm at a point at height of 15 cm from the bottom see figure The hole is at a height of 45 cm When the jar is filled with a liquid up to a height of 30 cm the same observer can see the edge at the bottom of the jar If the refractive index of the liquid is N 100 where N is an integer the value of N is 15 cm 15 cm 45 cm

Q No 19 If magnitude of dispersive power of two lens are 0 024 and 0 036 then focal length be for aberration free combination 1 2 3 30 cm 40 cm 30 cm 45 cm 10 cm 30 cm 20 cm 35 cm Correct Answer 2 Status unattempted

An object is placed 8 cm away from a mirror with focal length 12 cm Which of the following statements i corre O The image is virtual and on the opposite side of the mirror as the object O The image is real and on the same side of the mirror as the object O The image is real and on the opposite side of the mirror as the object O The image is virtual and on the same side of the mirror as the object

he po of time is given by R 4 sin 2nt i 4 cos 2nt j Where R is in meters t is in seconds and i and denote unit vectors along x and y directions respectively Which one of the following statements is wrong for the motion of particle 1 Path of the particle is a circle of radius 4 meter 2 Acceleration vectors is along R 3 Magnitude of acceleration vector is R where v is the velocity of particle 4 Magnitude of the velocity of particle is 8 meter second

1 An objective lens consist of i Short aperture and short focal length ii Large aperture and large focal length iii Short aperture and large focal length iv Large aperture and short focal length

A plane mirror is placed at a distance d from the screen on which spot is formed Ray is kept constant and mirror is rotated with constant angular velocity Then the acceleration off the spot on the screen is given by m Plane mirror 0 3 screen

When a thin convex and a thin concave lens are placed in closed contact their equivalent focal length is 50 cm The ratio of power of convex and concave lens is 2 1 then their individual focal lengths are 120 cm 40 cm 2 25 cm 50 cm 20 cm 40 cm 4 35 cm 45 cm

a Two plane mirrors are placed at an angle of 60 to each other An object is placed symmetrically between the mirrors Find the number of images formed by the mirror b What should be the angle between two plane mirrors such that the number of images formed is maximum How many images are formed in this case

A concave mirror of radius of curvature 40 cm is placed at the bottom of a tank of water with its optical axis vertical and the mirror facing upward Find the distance from surface of water of the final image in cm of a bird flying over the tank at a height of 60 cm above the surface of water Depth of water in tank is 20cm

1 8 A thin prism P with 4 and made from glass of refractive index 1 54 is combined with another thin prism P made from glass of refractive index 1 72 to produce dispersion without deviation The angle of the prism P is degree

Two bodies A and B are moving towards a plane mirror with speeds VA and v respectively as shown in the figure The speed of image of A respect to the body Bis A VA VB B VA VB C V D V V m m Normal 45 45 Normal

Directions The following questions consist of two statements I and II To answer these questions choose any one of the following four responses Codes A If both statements I and II are correct and Statement II is the correct explanation of statement I B If both statement I and statement are correct but statement II is not the correct explanation of Statement I C If statement I is correct but statement II is incorrect D If statement I is incorrect but statement Il is correct Assertion A thin lens is more powerful

of focal length f of the sun formed t is formed by a mal to its principal me screen without t and the screen in on the screen igned parallel to e A light ray is nt just inside one pincides with the number of time ing the first one 30 B Select a graph between v and jul for a concave mirror for real images object formed the mirrors is 2 Telegram ne questionpaper 3 4 lul

ce of that lane hen ent An optical fibre is made of glass fibre of refractive index 1 5 The outer coating of the glass fibre is made of material of refractive index 2 What is the range of angles of the incident rays with the axis of the pipe for which total internal reflection inside the optical fibre takes place 2 45 1 60 3 30

Figure shows two plane mirrors parallel to each other and an object O placed between them Then the distance of the first three images from the mirror M will be in cm 1 5 10 15 2 5 15 30 15 25 35 5 4 5 15 25 M 5cm 15cm M

PART C Physics 41 The optical power of a thin convex glass lens in air is 10D Its optical power when surrounded by air on one side and water on the other side and beam of light is incident from air side Hwater Hglass

A glass hemisphere 1 5 has a radius of curvature of 16 cm A small object O is located on its axis halfway between the plane and spheric surface The distance between two images when viewed along the axis from the sides of the hemisphere is mothe O horo mathong mathongo thongo mathongo B D cm cm mathongo mathongo mathon 10 13 pm