Optical Instruments Questions and Answers

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

At what distance do you think you should reasonably include the s distance in your calculation of f for the longer focal length lens For the smaller one Explain your rationale using Convex lens Equation 1 f 1 s 1 s f focal lens s object distance s image distance

For the two parallel rays AB and DE shown here BD is the wavefront For what value of wavelength of rays destructive interference takes place between ray DE and reflected ray CD D X E B 60 FC Mirror

A ray of light falling normally on the face AB of an equilateral glass prism having refractive index 3 2 placed in water of refractive index 4 3 will this ray suffer total internal reflection on striking the face AC

A police car moving at 22 m s chases a motorcyclist The police man sounds his horn at 176 Hz while both of them move towards a stationary siren of frequency 165 Hz Calculate the speed of the motorcycle if it is given that he does not observes any beats 1 2 3 Question Type Single Correct Type 33 m s 22 m s Police cur www Zero 22m s 176 Hz Motorcycle Stationary siren 165 hz

Focal length of simple microscope is 2 5 cm Find out its magnifying power when image is a At minimum distance of distinct vision b at infinite Question Type Single Correct Type 1 11 10 2 10 11 3 12 13

wo parallel disks 30 cm in diameter are separated by a distance of 5 cm in a large oom at 20 C One disk contains an electric heater that produces a constant heat flux of 100 kW m and 0 9 on the surface facing the other disk Its back surface is nsulated The other disk has 0 5 on both sides and is in radiant balance with the other disk and room Calculate the temperatures of both disks

Example 9 2 A mobile phone lies along the principal axis of a concave mirror as shown in Fig 9 7 Show by suitable diagram the formation of its image Explain why the magnification is not uniform Will the distortion of image depend on the location of the phone with respect to the mirror Ta B B A FIGURE 9 7

A ray of light travelling in air is incident at grazing incidence on a slab with variable refractive index n y k y32 1 1 2 where k 1 m 3 2 and follows path as shown in the figure What is the total deviation produced by slab when the ray comes out A 60 B 53 C sin 4 9 1m air air D no deviation at all

1 if a len is cut vertically into two equal halves then the intensity of transmitted light and aperture of the lens O half half respectively O remains same O half double respectively double half respectively

A gmy B rgmy Converging lenses make images smaller whereas diverging lenses make images larger Converging lenses always make virtual images whereas diverging lenses always make real images C When the thickness of the glass in a lens converges toward the center of the lens so that it is thinnest in the center it is a converging lens When it is fatter in middle it is a diverging lens D When two parallel rays of light pass through a converging lens the rays bend towards each other When they pass through a diverging lens the rays move ap from each other

9 The optical powers of the objective and eyepiece of a microscope magnification is equal to 100 and 200 respectively The microscope magnification is equal to 50 What will the magnification of the microscope be when the distance between the objective and eyepiece is increased by 2 Cm Ans 62

11 A symmetrical biconcave lens having radius of curvature R is made up of two different materials as shown in figure A parallel beam of light passing through the lens appear to diverge from two different points Find the distance between them R 2 4 4 R H H b 2 1 1 R4 1 2 4 1

The lens shown above is a convex diverge concave diverge convex converge lens and it will cause light rays to

Angular fringe width Let us solve some questions based on Young double slit experiment Example 8 Solution Two slits in YDSE are placed 2 millimeter from each other Interference pattern is observed on a screen placed 2 m from the plane of slits What is the fringe width for a light of wavelength 400 nm 2D d 0 4 mm In the above question what will be the angular fringe width Example 9 din il olution Angular fringe width will be B D 0 4 mm 2x10 radian 2 m ale Hof

In a diffraction pattern due to a single slit of width a the first minimum is observed at an angle 30 when light of wavelength 5000 is incident on the slit The first secondary maximum is observed at an angle of NEET 2016 1 sin 3 sin 3 4 1 2 3 2 sin 4 sin 1 4 9 2

Example 8 Consider the situation shown in figure The refractive index of medium is 3 2 and its radius of curvature is 30 cm PO PO 10 cm Find distance between O and O and seen by a O and b 0 Air 0 P 3 2 0 Medium

Problem 26 A convex lens and a convex mirror of radius of curvature 20 cm are placed coaxially with the convex mirror placed at a distance of 30 cm from the lens For a point object at a distance of 25 cm from the lens the final image due to this combination coincides with the object itself What is the focal length of the convex lens Solution For the image to form at O the rays after K25 cm Fig 16 66 M

ligure shows an icosahedron It consists of 20 equilateral triangles It has 12 vertices and 30 edges with 5 edges meeting at each vertex Each edge of an icosahedron shown in the figure is a 1 2 resistor The effective resistance between two adjacent vertices ab is B The effective resistance between two adjacent vertices is ab DIGITAL G 45 C The potential difference between cd is 8 15 D The potential difference between cd is 8 V V 11 30 30 11 2 2 Activate Windows

A vessel having perfectly reflecting plane bottom is filled with water 4 3 to a depth d A point source of light is placed at a height h above the surface of water Find the distance of final image from water surface

13 A planet revolves around the sun in an elliptical orbit of eccentricity e If T is the time period of the planet then the time spent by the planet between the ends of the minor axis and major axis close to the sun is a c 58 25 TR 2e Te b 7 7 7 1 d 4 3 2n A planet revolves around the sun in an elliptical c d 19 Ma A B C

Object Conve lens In the image above the object is more than two focal lengths from a convex lens what kind of image would be produced and which way would the image face a real image upside down a real image right side up a virtual image right side up

BANESWAR CENTRE 19 In the shown circuit all batteries have equal emf E Current through the 2R resistance is B 60 3E 2R 3R zero 20 In the circuit shown equivalent resistance between A and B is JEE Mai Advanced 2022 ENTHUSE COURSE Z 2R wwwwwwww www R R wwwwwwwww R 3R wwwww wwwwwww R R www www Ctivate V o Settings

A point source of light is placed at a distance h below the surface of a large dee lake Neglecting the partial reflection of light during refraction the percentage of light energy that escapes from the water surface is water 4 3

There is a small air bubble inside a glass sphere of 3 refractive index and radius 20 cm Bubble is at 2 distance of 5 cm from centre Find its apparent depth in cm from surface when viewed normally from the side where it is nearest to surface

Consider the following transactions with data items P and Q initialized to zero T read P read Q if P 0 then Q Q 1 write Q T read Q read P if Q 0 then P P 1 write P

CP 6 cm i e the mirror should be pla Problem 24 A convex lens of focal length 20 cm has a point object placed on its principal axis at a distance of 40 cm from it A plane mirror is placed 30 cm behind the convex lens as shown in the Fig 16 65 Locate the position of o image formed by this combination Solution Given f 20 cm u 40 cm IM KU IC 12 V M

A 50 cm square vertical plate is maintained at a constant surface temperature of 127 C on both sides and placed in a large chamber containing air at 1 7 atm and 27 C The walls of the large chamber are maintained at 22 C and the surface of the vertical plate is blackened on both sides so that its emissivity is 1 0 Calculate the total heat lost by both sides of the vertical plate expressed in watts

fish is rising up vertically inside a pond with velocity 4 cm s and notices a bird which is diving ertically downward and its velocity appears to be 16 cm s to the fish If refractive index of water is 3 then A velocity of bird with respect to ground is 9 cm s B velocity of fish with respect to bird is 15 cm s C velocity of bird with respect to ground is 12 cm s D velocity of fish with respect to bird is 12 cm s

In the diagram shown below the rays passing through the concave lens become parallel to the principal axis If focal length of the convex lens is 30 cm the focal length of concave lens will be 1 10 cm 2 20 cm 3 30 cm 4 40 cm B 10 cm

Length of barrel of a gun is l 5 0 m and mass of a shell fired is mo 45 Rg During firing combustion of the gun powder takes place at a constant rate r 2 0 x 10 kg s the gun powder is completely transfor med into gas of average molar mass M 5 0 x 10 2 kg mol temperature T 1000 K of the gases remain fairly constant and displacement of the shell inside the barrel is proportional to ta t is time and a is a constant Neglecting all forces other than force of the propellant gases during firing find the muzzle velocity of the shell Aus 3 4 R T l 1 3 issomle

Two mirrors M and M make an angle with line AB A point source S is kept at a distance r from the point of intersection of mirrors A small hemispherical annular mask is kept close to S so that no ray emanating from S directly reaches the screen kept at a distance b from the source Interference pattern of rays reflected from M and M is observed on the screen Find the fringe width of this interference pattern wavelength of light being emitted by source A C 2 b 2rsin b 2rsin 20 b rcos 20 2r sin 20 B D M m S b 2r cos 26 2r sin 20 2 b 2rcos 20 rsin 20 b b Sc hemispherical annular mask 27 Surfac

A thin lens made of glass refractive index 1 5 of focal length f 16 cm is immersed in a liquid of refractive index 1 42 If its focal length in liquid is f then the ratio f f is closest to the integer 1 1 2 5 3 9 4 17

A 4 8 cm B 3 4 A 2 cm high object is placed at a distance of 20 cm from a concave mirror If the imag formed by the mirror is inverted and height is 4 cm then the focal length of the mirro would be A 12 3 cm B 13 3 cm C 14 5 cm D 5 2 cm C 1

Consider the following statements i The focal length of a concave mirror depends on colour of light ii If a spherical mirror is immersed in a liquid its focal length will remain unchanged B Both i and ii are false D i is false ii is true A Both i and ii are true C i is true ii is false

through a polariser and analyser which are at an angle of 45 with respect to each other The intensity of polarised light coming from analyser is 5W m The intensity of unpolarised light incident on polariser is 1 5 3 W m 3 20 W m 2 10 W m 3 4 5 W m

Joule s Law is useful in devices that make use of heating effect of electricity Let s solve some mathematical problems which are related to Joules Law How much will be the heat developed if 0 2 A current flows through a conductor of resistance 200 2 for 5 minute H I Rt R 200 2 I 0 2 A t 0 2 200 300 2400 J Heat generated 2400 J 5 60 s 300 s

4 A ray of light is going from air to glass such that the reflected light is found to be completely plane polarized Also the angle of refraction inside the glass is found exactly equal to the angle of deviation suffered by the ray The refractive index of the glass is 11 5 2 2 3 3 4 4 3

3 sin 8 Light takes 1 second to travel a distance x cm in vacuum and the same light takes 1 second to travel 10x om in medium The critical angle for the corresponding medium is 2 sin 1 sin IN 3 sin 10 106 4 sin 101 10 ay helow the surface of a take If the critical angle is 49 then the fish could see thin

81 In a compound microscope if the objective produces an image I and the eye piece produces an image I then a I is virtual but I is real b I is real but I is virtual c I and I are both real d I and I are both virtual

30 A camera objective has an aperture diameter d If the aperture is reduced to diameter d 2 the exposure time under identical conditions of light should be made a 2 fold b 2 fold c 2 2 fold d 4 fold

through which the reflected ray gets rotated when the mirror is rotate by an angle of 600 keeping the incident ray constant ii the angle through which the reflected ray gets rotated when the incident ray is rotated by an angle of 30 in clockwise direction mirror is fixed iii the angle through which the reflected ray gets rotated when the mirror is rotated by an angle of 600 clockwise as well as the incident ray is rotated by an angle of 30 in anti clock wise direction A i 120 C i 120 ii 60 ACW ii 60 ACW A ray of light travel f iii 120 ACW iii 150 ACW B i 120 D i 120 ii 30 ACW ii 60 CW iii 150 CW iii 120 CW

A ray of light is incident at surface P at an angle e slightly greater than the critical angle between medium A and C where 3 Now a slab of refractive index is inserted between A and C as shown then choose the correct alternative 44 A B H 77 C 3 0 A For TIR will take place at surface P B For TIR will take place at surface Q C For 3 light will be transmitted to A D For light will not be transmitted to A P

In a normal eye the retina is about 2 00 cm behind the lens of the eye Suppose the lens must accommodate to clearly focus an image on the retina of an object 1 00 m in front of the eye What is the power of the lens a 1 5 Diopters b 51 Diopters C 49 Diopters d 101 5 Diopters

QA plane mirror is placed with its plane at an angle of 30 with the y axis Plane of the mirror is perpendicular to the xy plane and the length of the mirror is 3m as insect moves along x axis starting from a distance point with a speed 2cm s the during of the time for which the insect can see its own image in the mirror is 3cm 30 X

The dashed part of the lens is cut and kept on the x axis as shown in the diagram If parallel paraxial rays are falling on this system then the coordinate of image formed after refraction from both the lenses is 30 1 If x 2 5 then all the distance is in cm Assume lens have no spherical aberration X y 0 0 X

Column I A Hypermetropia B Myopia C Astigmatism D Presbyopia 1 2 3 4 Column II A A 3 B 1 C 2 D 4 B A 4 B 3 C 2 D 1 C A 1 B 2 C 3 D 4 D A 3 B 4 C 1 D 2

Example 128 You are given two converging lenses of focal lengths 1 25 cm and 5 cm to design a compound microscope If it is desired to have a magnification of 30 find out separation between the objective and the eyepiece CBSE OD 15 Solution Here fo 1 25 cm f 5 cm D 25 cm m 30 When the final image is formed at the near point of the eye the magnifying power of the compound microscope is or m 30 L D H 1 9 1 fo fe L L 1 25 25 1 5 30 1 25 6 25 cm b or So a

Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space The period of revolution is 3 12 d 2 3Gm 3Gm d d 2 2 3Gm 4 2t 3Gm d H

Question 32 An object S is placed at a distance of 20 cm from a convex lens of focal length 15 cm as shown in the figure where should a convex mirror of focal length 25 cm be placed from the lens so that a real image is formed on the object itself 20 cm t Options 20 cm 10 cm 40 cm 25 m