Geometrical Optics Questions and Answers

An object is located in a fixed position in front of a screen Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm The size of the images in two situations are in the ratio 3 2 What is the distance in cm between the screen and the object A B C 124 5 144 5 65 00

Ans 0 15 m infront of the lens 28 A convergent beam of light passes through a diverging 1 lens of focal length 0 2 m and comes to a focus on sithe axis 0 3 m behind the lens Where would the beam have been focussed in the absence of the lens 29 Ans 0 12 m behind the position of the lens DA long A beam of light

A planoconvex lens becomes an optical system of 28 cm focal length when its plane surface is silvered and illuminated from left to right as shown in Fig A If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig B it acts like an optical system of focal length 10 cm The refractive index of the material of lens is A B skipped C 1 50 1 55 1 75 QUESTION 1 2 6 O Correct 0 7 MY PERFOR SCORE 1 00

A particle is oscillating on the X axis with amplitude 2 cm about the point x 10 cm with a frequency w A concave mirror of focal length 5 cm is placed at the origin see figure xo 10 cm x 0 Identify the correct statements 1 The image executes periodic motion 2 The image executes non periodic motion 3 The turning points of the image are asymmetric w r t the image of the point at x 10 cm 100 4 The distance between the turning points of the oscillation of the image is 21 A B skipped C 1 4 1 3 4 2 4 cm QU M

A tube of length 30 cm has its inner lateral surface blackened Two lenses of focal lengths 10 cm and 20 cm are fixed at the ends of the tube For same beam intensities of spots on screen are I and 1 for arrangement 1 and arrangement 2 If the ratio of I I is of the form N find N I2 Beam 10 cm Tube 20 cm Screen Arrangement 1 Beam 20 cm Tube 10 cm Screen Arrangement 2

The object is moved from infinity to focus in front of a concave mirror Which of the following graphs depicts the correct relation between the magnitude of distance of the object from the mirror u and the distance of the image from the mirror v Give reasons for your answer a b d Practice U OSKU

An equi biconvex lens u 1 5 of focal length 20 cm is cut into two parts and placed in contact as shown in the figure A liquid of refractive index 1 3 is filled between the two parts of lens Then find the equivalent focal length of the combination in cm

A plane mirror makes an angle of 30 with the horizontal If a vertical ray strikes the mirror find the a between the mirror and the reflected ray

11 A plane mirror is moving with velocity 41 53 8k A point object in front of the mirror moves with a velocity 31 43 5k Here k is along the normal to the plane mirror and facing towards the object The velocity of the image is 1 31 4 5k 2 31 43 11k

A normal human eye can see an object making an angle of 1 8 at the eye approximate height of object which can be seen by an eye placed at a distance of 1 m from the object is TU X Find the value of x 1 8 1m cm

5 In the diagram shown the height of the lens is 5cm and its focal length is 10cm A point objec has been placed at a distance 30cm from the lens If the object is a source of light then what is the area of the screen that will receive light A 5 B 25 3 C n 5 2 D None O 5cm The distance of the screen from the lens is 40 cm

A beam of converging rays is incident on a convex mir ror of focal length 30 cm In the absence of the mirror the converging rays would meet at a distance of 20 cm from the pole of the mirror If the mirror is situated at the said position where will the converging rays meet

The image of the flame of a candle due to a mirror is formed on a screen at a distance of 9 cm from the can dle The image is magnified 4 times Determine the nature position and focal length of the mirror

A magnifying lens is of focal length 10 cm At what distance from the lens an object should be placed to view the object at maximum magnification 40 7 cm 10 cm 50 cm

A point object O is placed at a distance of 0 3 m from a convex lens of focal length 0 2 m It is then cut into two halves each of which is displaced by 0 0005 m as shown in figure J 4 0 3 m Image will be formed from the lens at a distance of 30 cm B40 cm m 2x0 0005 m 50 cm

A concave mirror of focal length 10 cm and a plane mirror are placed at a separation of 22 5 cm as shown in figure At what distance in cm from the plane mirror an object should be placed so that the first image by both the mirrors coincides

place e g e g 06 23 9 25 0 00 33 00 30 30 27 27 30 A uniform thin rod of length 10 cm is placed along the principal axis of a concave mirror of radius of curvature 20 cm If the nearer end of the at a distance of 15 cm from pole of mirror then the value of length of image of rod is given by 40 cm Find the value of x X

In a YDSE experiment 2 540 nm D 1m d 1 mm A thin film is pasted on upper slit and the central maxima shifts to the point just in front of the upper slit What is the path difference at the centre of the screen A 540 nm B 270 nm C 500 nm D 810 nm

n equi biconvex lens p 1 5 of focal length 20 cm is cut into two parts and placed in contact as shown in the figure A liquid of refractive index 1 3 s filled between the two parts of lens Then find the equivalent focal length of the combination in cm

Section of a refracting surface is shown in figure The section is symmetrical about x axis Refractive index of medium on right of the surface is n with respect to the medium on left of the surface Parallel monochromatic light rays are incident on the surface as shown in figure and the refracted rays are focused at F at a distance f from origin O of the co ordinate system shown in figure The equation y x of shape of the section shown is found to be n 1 x n y Bn n 1 fx 0 Find B 2 y F X

The system contains a box of length L 20 cm On the left end of the box a plane mirror is placed and on the right hand a convex lens of focal length f is placed An object is placed at a distance x from the plane mirror Two images are formed for the system One is direct refraction through the lens and other is after reflection from plane mirror and then refraction through the lens The size of fina images formed is same A 15 cm Of Q The minimum separation between final two images formed is B 12 cm L C 40 cm D 25 cm

Two plane mirrors are inclined at angle 8 If any ray incident on one mirror becomes anti parallel after reflection from other mirror then angle 8 can be O8 90 45 0 90 O 0 45 08 90 31

A point object is placed in the arrangement shown The distance of image formed by lens 2 from its optical centre is f 20 cm Object 30 cm 1 20 cm 3 40 cm Lens 1 45 50 cm f 10 cm 30 cm 2 30 cm 4 60 cm 777 Lens 2

Media Water Refractive 1 33 index Glass 1 5 Diamond 2 42 low answer the following A In which medium the critical angle will be maximum B In which medium the critical angle will be minimum C Calculate the critical angle of diamond Kerosene 1 44 Ice 2 29

For a ray incident on a plane mirror as shown if mirror is rotated by 1 in direction given in the diagram reflected ray rotates by 60 O 1 clockwise 7777M M O 1 anticlockwise O 2 clockwise 2 anticlockwise

a 100 b 101 c 1 10 If a concave mirror of focal length f is placed at a distance of d from a convex lens of focal length f2 A light ray coming from infinity is falling on this combination and returns to infinity The distance d must equal d 2f f a 1 1 b 1 h C 21 f

8 A point object is performing circular motion on a circle of radius R as shown in the diagram The center of the circle is at a distance of 15cm from the lens of focal length 10cm The plane of the circle is perpendicular to the axis of the lens If the object is moving with constant speed of 1m s then answer the following questions i What is the radius of the image circle A R C 3R 2 ii Y What is the speed of the image A 2 m s C 0 5 m s B 2R D None B 1 m s D None

1 The diagram shows two lens placed at a distance 50cm from each other Find out the final position of the image of the object shown The distance of the object from the lens is 20cm and the focal length of both the lens is 10cm A 15 m right to the second lens B 30 cm right to the second lens C 15 cm right to the second lens D None 0 f the final image

The diagram shows two lenses having focal length 10cm and 10cm A line object of length 1cm is placed perpendicular to the axis The distance of the object from the first lens is 20cm and the separation between the lens is 5cm Find out the followings i Position of the final image A 30 cm left to concave lens B 30 cm right to concave lens C 15 cm left to concave lens D None ii A 1 cm Final length of the image B 2 cm OX C 1 2 cm D None

9 In the diagram shown a point object O has been placed on the axis of the left lens at a distance 20cm The right lens is at a distance 50cm from the left lens The axis of the two lenses are separated by a distance of 0 1cm Both the lens have focal length equal to 10cm If the optical center of the left is taken as the origin then what will be the coordinates of the final image position A 75 0 15 B 65 0 15 D None C 45 0 15

An equiconvex lens of focal length 10 cm and refractive index 1 5 is cut vertically into two equal pieces They are placed as shown with a liquid of refractive index 3 between them What is the focal length of the combination A 10cm B 10 4 10 3 D None

A beam of light has a small wavelength spread X about a central wavelength The beam travels in vacuum until it enters a glass plate at an angle relative to the normal to the plate as shown in the figure 0 86 Vacuum Glass The index of refraction of the glass is given by n X The angular spread S0 of the refracted beam is given by

What type of a spherical mirror is required to project the image of the flame of a candle on a wall 9 ft away from the flame Determine the position of the mirror and its focal length concave at a distance of 3 ft from the flame opposite to the wall 2 4 ft

A L 2 3 In the diagram shown the lens has focal length 3L An object is placed at a distance 4L from the lens A glass slab is placed between the lens and the object What is the refractive index of the slab if the image of the object is obtained at infinity The width of the slab is 2L A 3 2 C 4 3 B 2 D None OBJECT

An equi biconvex lens 1 5 of focal length 20 cm is cut into two parts and placed in contact as shown in the figure A liquid of refractive index 1 3 is filled between the two parts of lens Then find the equivalent focal length of the combination in cm

6 A planet subtends an angle min at the pole of a concave mirror The diameter of the image of the planet formed by the mirror is 4 mm Calculate the radius of curvature of the concave mirror 14 4 m S

below OI CD are put in contact as shown in figure i and ii A C fig i fig ii The resulting focal length of fig i and ii will be Teng 0 f f B 0 D f 2 as 8

8 An arrow of length 15 cm is placed along the axis of a con cave mirror Its sharp end is at a distance of 30 cm from the mirror and the radius of curvature of the mirror is 20 cm Calculate the magnification of the image of the 0 143 arrow

A uniform thin rod of length 10 cm is placed along the principal axis of a concave mirror of radius of curvature 20 cm If the nearer end of the rod is at a distance of 15 cm from pole of mirror then the 40 value of length of image of rod is given by cm X Find the value of x

3 The diameter of the moon is about 2160 m When the moon s distance from a concave mirror is 35 36 104 km an image of diameter 1 5 cm of the moon is formed What is the radius of curvature of the mirror 3 m

Figure shows the behaviour of light rays with respect to a plano convex lens whose plane surface is silvered as shown in the figure If the refractive index of the material of the lens is 1 5 the radius of curvature of the curved part of the lens is A 30 cm C 15 cm B 5 cm D 60 cm 30cm

ance and image distance From the mirror equation we get or Since or 1 1 V U u V 1 m m m 1 1 f u 12 u u f f f u f u f or V f u V Again the equation can be written as V or u f f U u or v f f V u u f

a convex lens of focal length 30 cm If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it the Final image would be formed at a distance of 1 20 cm from the lens it would be a real image 2 30 cm from the lens it would be a real image 3 30 cm from the plane mirror it would be a virtual image 4 20 cm from the plane mirror it would be a virtual image

A convex lens of focal length 100 cm is cut along the principal axis and a thin layer of thickness 1 mm is removed and then put together to form a composite lens as shown in figure Now a light source is placed at distance 50 cm from the lens and a screen at 100 cm behind the lens If wavelength of light emitted is 600 nm then the fringe width comes out to be mm Find the value of B 1 mm Correct answer 01 20 Source 50 cm 100 cm Screen

35 A marginal ray falls upon a concave mirror of radius of curvature 20 cm as shown in figure Find distance CM in cm 43 CH 1 2 30 J ive G 30 60 e 30 tive 1 10 20 3 3 e 30 30 C tanso P 30 300 M ER 20 cm CM 2 16 4 10 3

A particle executes S H M in front of a concave mirror of radius 1 m about the centre of curvature along the axis with very small amplitude a The amplitude of oscillations of the image is 1 a 2 2a 3 2 4 None of these Face 800S N

A ring of radius R is floating on the surface of a liquid of refractive index 3 A point source of light is placed on the axis of the ring at a depth 3R The radius of the shadow of the ring on the ceiling at a height 5R from the surface of the liquid will be 1 5 3R 3 1 3 R 2 1 5 3 R 4 10 3R

A ray of light is incident on an equilateral prism at an angle of incidence i such that it is incident normally on other refracting faces Find i take glass 2 1 30 2 45 3 60 4 Not possible

The magnifying power of an astronomical telescope in normal adjustment is 100 The distance between the objective and the eyepiece is 101 cm The focal length of the objectives and eyepiece is a 10 cm and 1 cm respectively b 100 cm and 1 cm respectively c 1 cm and 100 cm respectively d 1 cm and 10 cm respectively

equation State clearly the three salient features observed in photoelectric effect which can be explained on the basis of the above equation 22 A small illuminated bulb is at the bottom of a tank containing a liquid of refractive index up to a heigh Find the expression for the diameter of an opaque disc floating symmetrically on the liquid surface in ord cut off the light from the bulb SECTION D