Wave Optics Questions and Answers

ellets of mass 2 0 g are fired in parallel paths with peeds of 130 m s through a hole 3 0 mm in ameter Part A How far from the hole must you be to detect a 1 0 cm diameter spread in the beam of pellets Express your answer to two significant figures and include the appropriate units SH

40 In the figure shown in YDSE a parallel beam of light is incident on the slit from a medium of refractive index n The wavelength of light in this medium is 2 A transparent slab of thickness t and refractive index n is put infront of one slit The medium between the screen and the plane of the slits is n The phase difference between the light waves reaching point O symmetrical relative to the slits is n 2 V A n3 n t n 2 3 n n C t B D 2 2 n n t 2in 2 n n t 7 l n

Q 10 Two coherent sources of light are placed at points Sa 2 214 4a 3 A 12 5a 0 and 0 Wavelength of the light is 2 How many maximas will be obtained on a CD planar circle of large radius with centre at origin B 15 C 16 D 14 I YROR 200

The radius of the central bright spot in t he diffraction pattern of a circular hole of diameter d with light of wavelengt h is r and the distance between the ci rcular hole and screen is D Now the wh ole set up is immersed in a liquid of refr active index u and the distance betwee n the hole and the screen is reduced b y 2 times the radius of central bright sp ot reduced by 4 times The value of u is

Beyond Fresnel distance A B D Diffraction becomes insignificant Diffraction are smaller compared to the size of beam Spreading of light due to diffraction dominates over ray optics Ray optics is valid

monochromatic In a modified Young s double slit experiment a uniform and parallel beam of light of wavelength 6000 and intensity 10 W m is incident normally on two circular apertures A and B of radii 0 001 m and 0 002 m respectively A B F h A perfectly transparent film of thickness 2000 and refractive index 1 5 for the wavelength of 6000 is placed in front of aperture A see figure Calculate the power in watt received at the focal spot F of the lens The lens is symmetrically placed with respect to the aperture Assume that 10 of the power received by each aperture goes in the original direction

In Column I the parallel rays are incident on some optical device and in Column II the shape of emergent wavefronts are shown Select incorrect match Column I 1 2 3 Column II

34 In Young s double slit experiement the point source S is placed slightly off the central axis as shown in the figure If A 500 nm then match the following A B D 2 mm EFELER T 1 m 2 m Column 1 Nature and order of interference at point P OP 10 mm Nature and order of interference at point O If a transparent paper refractive index 1 45 of thickness f 0 02 mm is pasted on S i e one of the slits the nature and order of the interference at P After inserting the transparent paper in frout of slit S the nature and P Q R y 10 mm Column II Bright fringe of order 80 Bright fringe of order 262 Bright fringe of order 62 S Bright fringe of order 280

A monochromatic point source S of wavelength is kept in front of a plane mirror MM Interference is observed at poin P of two waves SAP and SP It is given that AB 14x AC 8x BS 2x SD 2 11 2 x The minimum value of x for which the maximum intesnity is obtained at point P after interference is A S B M O A 03 10 3 2 M P D

Q 2 A linearly polarised electromagnetic wave given as E Eo i cos Assuming that the material of the wall is optically inactive the reflected wave will be given as a Er Epic COS kz wt b E Epi cos kz wt c E Eoi cos kz d E Ei sin kz Internet wt 55 From NC wt is incident normally on a perfectly reflecting infinite wall at z a

In the Young s double slit apparatus shown the distance between the two slits is d Then distance of the source from the slit plane is D The distance between the screen and slit plane is D Monochromatic light of wavelength X is emitted by the source The condition for maxima at point P in front of upper slit is Given d D d D d Source S O O 12 2 d d 82 2 2n 1 2 D D D D n d n d d D n ola 2 Screen

A YDSE experiment is used to measure the wavelength of light used The distance between screen and slits is measured by a meter scale with least count 1mm The measured distance is 1 500 m The distance between the slits is measured by a micrometer of least count 0 01 mm The distance between slits is measured to be 0 33 mm The fringe width is measured by the same micrometer It comes out to be 2 50 mm The wavelength of light is

A concave lens of focal length 20 cm is placed 20 cm in front of a plane mirror as shown below Light from a very far away source is falling on the lens The p size of concave lens is sufficiently large he position of final image formed by combination is Consider the f 20 cm Educa M 1 10 cm in front of mirror 3 15 cm in front of mirror 20 cm 2 5 cm in front of mirror 4 5 cm behind the mirror The length of a wire is increased to twice while keeping its volume constant The resistivity of wire become 1 Double 2 Four times 3 Sixteen times 4 Remains unchanged

biprism deduce the position of the zero order fringe Why is it much more difficult to see interference fringes for light reflected from a the piece of glass than from a thin film Would it be easier if monochromatic light were use

3 A Mooney rhomb n 1 64 is shown below Show that it works as a Fresnel rhomb if the incoming plane wave is linearly polarized at 45 to the plane of incidence the emerging beam is circularly polarized 60

The intensity of a plane electromagnetic wave is 5 W m2 It is incident on a perfectly reflecting surface Find the radiation pressure 1 3 33 10 9 N m 2 3 33 10 8 N m 3 8 0 10 8 N m 4 8 0 10 9 N m

Newton s rings are observed in reflected light using light of wavelength 5890 The radius of the convex surface of the lens is 100 cm A liquid is put between curved surface of lens and plate The diameter of 10th ring is 4 2 m m Calculate the refractive index of liquid when a ring is dark and b ring is bright Ans 1 335 and 1 268

4 a A plane transmission grating having 5000 lines per cm is being used under normal 8 2 Marks incidence of light 1 What is the longest wavelength of light for which a spectrum can be seen 2 What is the highest order spectrum that can be seen for the light of wavelength 6000 3 If the width of opaque parts is double than that of transparent parts of the grating then which orders of spectra will be absent 4 If 90 of the width of the ruled width of the grating is covered what will happen to the observed spectrum b Two nicols are first crossed and then one of them is rotated through 60 Calculate the percentage of incident light transmitted

48 Two identical coherent sources are placed on a diameter of a circle of radius R at separation x R symmetrical about the center of the circle The sources emit identical wavelength each The number of points on the circle of maximum intensity is x 5x

b Why is it much more difficult to see interference fringes for light reflected from a thick piece of glass than from a thin film Would it be easier if monochromatic light were used

6 Two plane glass surfaces in contact along one edge are separated at the opposite edge by a thin wire If 20 interference fringes are observed b w these edges in sodium light at normal incidence what is the thickness of wire sodium 5893A

6 Suppose in a double slit experiment with a light of wavelength 600 nm separation between the slits is 0 2 mm and the interference fringes are seen on a screen 1 2 m away Find the distance of the 3rd order maximum from the central zeroth order maxima What will be the value of this distance when the experiment is performed under water r i 1 33 ptongo between the slits is 0 1 mm and the perpendicular

In wavelength division multiplexing O different time signals are transmitted over single optical fiber multiple optical signals are transmitted over single optical fiber Omultiple frequency signals are transmitted over single optical fiber multiple high frequency carrier signals are transmitted over single optical fiber

A point object approaches towards a convex mirror of focal length 2 m with a speed of 10 m s The speed of the image of the object when the object is at a distance 20 m from the mirror is 8 3 cm s 0 8 m s 10 8 m s O 20 m s

In the figure shown the radius of curvature of the left right surface of the concave lens are 10 cm 15 cm respectively The radius of curvature of the mirror is 15 cm equivalent focal length of the combination is air D water n 4 3 Glass n 3 2 A the system behaves like a convex mirror of focal length 18cm B the system behaves like a concave mirror of focal length 18cm C the system behaves like a convex mirror of focal length 36cm D the system behaves like a concave mirror of focal length 36cm

The formula for refraction at a curved transparent surface is given below in usual notation i R iii Specify the a meaning of each symbol in the formula b sign convention you use 5 marks ii A small goldfish is viewed through a spherical glass fishbowl of diameter 30 cm filled with water refractive index 4 3 Use the formula given above to determine the apparent position and magnification of the fish s eye when its actual position is a at the center of the bowl b halfway between the center and the glass nearer to the eye along the line of sight Assume that the glass is thin enough so that its effect on the refraction may be neglected 10 marks Illustrate the image location in each of the cases a and b above with a clearly labeled ray diagram using a rough scale Are the images real or virtual 5 marks

6 a A diffraction grating used at normal incidence gives a yellow line 6000 in a certain spectral order superimposed on a blue line 4800 of next higher order if the angle of diffraction is sin 3 4 calculate the grating element 5 5 Marks

Light of wavelength 250 nm falls on a metal having binding energy 2 6 eV Find the maximum kinetic energy in eV of the photoelectrons ejected from this metal h 6 6 10 34Js 1eV 1 6 10 19 J 0 eV O 7 50 eV 2 35 eV 4 95 eV

Microwaves are produced by motion of charges in Accelerated motion conducting wires Special vacuum tubes called klystrons Hot bodies and molecules Hot bodies and special lamps

For a parallel beam of monochromatic light of wavelength X diffraction is produced by a single slit whose width a is of the order of the wavelength of the light If D is the distance of the screen from the slit the width of the central maxima will be 2Da 7 O 2D D

ii Two polarising plates have polarising directions parallel so as to transmit maximum intensity of light Through what angle must either plate be turned if the intensity of transmitted light is dropped by one third 6

0 In Young s double slit experiment one of the slit is wider than other so that amplitude of the light from one slit is double of that from other slit If I be the maximum the resultant intensity I when they interfere at phase difference o is given by m intensity a m 4 5 cos q c ELO Im b b 3 1 2 cos 1 4 cos d 1 8 cos 2

5 A plane mirror produces a magnification of A 1 2 1 501 ith 201 3 Zero 4 Between 0 and 1

The refractive index of water with respect to air is index of water with respect to glass is 08 9 0 1 2 02 86 3 and the refractive index of glass with respect to air is Then the refractive Marks 4 1

The nergy of a photon of EM radiation is of order of 1 Kev To which part of spectrum does it Jeng y ray 3 Infra red rays 2 x ray 4 U V rays

picture showing images f ormed by point object in a myopic ey e What will be the image formed by a LINE OBJECT in a myopic eye De scribe the nature of the IMAGE OBTA INED ON RETINA if the LINE OBJECT is 1 CM FAR from the far point of the myopic eye i e the image is FORME D IN FRONT OF THE RETINA with a diagram

A thin paper of thickness 0 02 mm having refractive index 1 45 is pasted across one of the slit in a Young s double slit experiment The paper transmits 4 9 of light falling on it ight 600 nm A Amplitude of light wave transmitted through the paper will be 2 3 time of incident wave S The ratio of maximum and minimum intensity in the fringe pattern will be 25 S The total number of fringe crossing the centre if an identical paper is pasted on the other slit is 15 D The ratio of maximum and minimum intensity in the pattern will be 5

In Michelson s interferometer what is the effect on fringe patterns if the two mirrors are not perpendicular to each other In Michelson s interferometer 200 fringes cross the field of view when the movable mirror is displaced through 0 05896 mm Calculate the wavelength of the monochromatic light used

The radius of curvature for a convex lens is 40 cm for each surface Its refractive index is 1 5 The focal length of the lens will be 40 cm 20 cm hr mi 80 cm

A parallel beam of light of wavelength 600 nm falls normally on a slit of width a Find the value of a so that the first order diffraction maximum occurs at an angle of 30 1 1 1 X 10 m 3 1 3 X 10 m 2 1 2 X 106 m 4 1 4 X 106 m

5 In lens displacement method lateral magnifications obtained are 2 and 0 5 If separation between position of lenses is 30 cm then focal length of the lens is 1 30 cm 3 15 cm 2 20 cm 4 10 cm

8 If a parallel beam of light of circular cross section having radius 10 mm falls on the surface of glass sia 3 2 U at an angle 30 with the surface of slab then the radius of refracted beam is about 1 12 5 mm 14 5 mm 2 13 7 mm 416 2 mm

2 When light is refracted into a rarer medium from a denser medium O its wavelength increases energy and frequency remain unchanged its wavelength decreases energy decreases but frequency remains unchanged its wavelength and frequency both decreases its wavelength and frequency both increases

Given 11 70 micrometer Distance of light source from upper slit 12 90 micrometer Distance of light source from lower slit Wavelength of light used 500 nanometer Distance between slits d 10 micrometer Distance of screen from slit 2 metres S A 30 B 40 C 50 D 60 N 5 S Wh below the number of maxima appearing on the screen will be 524 16 1 0 1 D

Two coherent sources are emitting light of wavelength A 5000 The separation between the sources is 2 5 mm and the separation between the source and the screen is 2 m Then which of the following are correct Screen 4 90 S D The position of 3000th order bright fringe from C is 8 3 m The position of 2500th order bright fringe from C is 2 3 m The position of 5th bright fringe from C is 0 08 m include the bright fringe at C The shape of fringes on the screen are circular

between the Two coherent sources are emitting light of wavelength A 5000 A The separation between the sources is 2 5 mm and the separation betw source and the screen is 2 m Then which of the following are correct Soem OC WOP C The position of 3000 The position of 2500 The position of order bright fringe from C is 8 3 m order bright fringe from C is 2 3 m 5 bright fringe from C is 0 08 m include the bright fringe at C n The shape of fringes on the screen are circular

4 5 The refractive index of water with respect to air is and the refractive index of glass with respect to 3 air is 33292 Then the refractive index of water with respect to glass is 1 9 8 2 8 9 3 1 4 2

6 Find the number of maxima and minima for the following arrangement which is detect by detector Detector 1 60 2007 310 20 116 1 18 18 3 20 20 S 4 92 Sz 280 320 1 290 3 2 18 20 4 16 18 Co

the figure shown below there is an equilateral glass prism ABC of which point C is attached with plane mirror held at an angle 0 with the horizontal The deviation suffered by the ray from the prism is 10 The angle of incidence is 30 The value of angle 0 is B A C 0 Plane mirror

A clear sheet of polaroid is placed on the top of similar 3 5 sheet so that their axes make an angle sin other The ratio of intensity of the emergent light to that of unpolarised incident light is O 16 25 O 9 25 with each 4 5