Wave Optics Questions and Answers

Multiple Choice only one answer is correct An electron is described by a wave function given by v x 2 ae x Determine the probability of finding the particle between the limits 0 x al a 0 393 b 0 487 c 0 513 d 0 948

Answer Type 1 Two glass plates are touching at one end and separated by a thin wire at the other end When a monochromatic parallel beam of wavelength 4200 incident normally on the glass plates is reflected an interference pattern of 30 fringes are observed If the wavelength of light used is taken 7000 instead of 4200 the number of fringes observed will be a 50 b 40 c 30 d 18

1 An isotropic point light source S of power P located a distance d specially designed non absorbing non dispersing and non refl lens This lens converges all the radiant energy coming from the into a beam parallel to its optical axis Find magnitude of the fo radiation pressure on the lens

Q 2 The following question consists of two statements Assertion and Reason 1 A Both assertion and reason are true and the reason is the correct explanation of assertion B Both assertion and reason are true but the reason is not the correct explanation of assertion C Assertion is true but reason is false D Assertion is false but reason is true 1 pc 2 1 Assertion An object is placed at a distance of f from a convex mirror of focal length f its image will formed at infinity Reason the distance of image in convex mirror can never be infinity O A OB O C C

A screen is placed 2m away from the 2 points lens to obtain the diffraction pattern in the focal plane of the lens in a single slit diffraction experiment What will be the slit width if the first minimum lies 5 mm on either side of the central maximum when plane light waves of wavelength 4000 are incident on the slit O 0 16 mm O 0 26 mm O 0 36 mm O 0 46 mm

a fluid N Displacement leads over Pressure wave by 90 degree Pressure wave and displacement are in same phase Pressure wave leads over displacement by 90 degree Pressure wave and displacement are in opposite phase

A linear object of length 10cm has been placed horizontally on the axis length 20cm The center of the line is at a distance 40cm from the lens What is the length of the image A 32 9 cm B 32 5 cm C 32 3 cm D None A B

Find the missing order for a double slit Fraunhofer Diffraction pattern if the slit widths are 0 2 mm separated by 0 6 mm O 1st 5th 9th 2nd 6th 10th 3rd 7th 11th O 4th 8th 12th N

29 A parallel beam of green light of wavelength 546 nm passes through a slit of width 0 40 mm the transmitted light is collected on a screen 40 cm away What will be the distance between two first order minima a 2 6 mm c 1 7 mm b 1 8 mm d 1 1mm

The intensity of a point source of light S placed at a distance d in front of a screen A is I at the center of the screen The light intensity at the center of the screen if a completely reflecting plane mirror M is placed at a distance d behind the source as shown in figure assume no interference found to be N times Io 9 Find the value of N M d

Interference pattern in reflected light for normal incidence on a wedge shaped air film is seen using bichromatic 2 5896 A 5890 source of light The angle of wedge is 0 25 of arc Find out the minimum distance from the edge of the wedge at which maximum due to each wavelength coincides CO3

No work is done and kinetic energy also does not change A long narrow horizantal silt is placed 1mm above horizontal plane mirror the interference between the light coming directly from the silt and that after reflection is seen on a screen 1m away from the silt if X 700nm then fringe width is Q 12 Option 1 20mm Option 2 25mm Option 3 30mm Option 4 35mm Correct Answer 35mm

The length of plane mirror is 1cm The wavelength of source is 5000 A The numbe of maxima formed on the large screen is n P is central point on screen the value of n 1 is S 5mm Im Plone mirror P Screen

In each situation of Column 1 and incident wavefront and its corresponding reflected or refracted wavefront is shown In column II the optical instrument used for reflection or refraction is given Always take the optical instrument t the right of incident wavefront The incident wavefront is moving towards rig Match each pair of incident and reflected refracted wavefront in column I wit the correct optical instrument given in column II Consider the shape of the refracted wave fronts in case of lens only between t second principal focus and lens virtual wave fronts are also taken into consideration same condition is applied in case of mirrors Column I Incident Reflected Refracted Wavefront wavefront L 1 A B C D 1 P Q R S Column II Optical instrument used r

A wedge of mass M can slide on two parallel rails A and B inclined at an angle to the horizontal In the middle of the rails and parallel to them runs a frictionless rod C that wears a light ring D The rod does not touch the wedge A light inextensible cord attached with the ring runs through a hole in the wedge without touching it then runs round an ideal pulley on the top of the wedge and finally attached to a block of mass m that can slide along the vertical face of the wedge without friction as shown in the figure Coefficient of friction between the wedge and the rails is Initially the system is held motionless and then released Find the acceleration of the block Acceleration due to gravity is g

7 A mixture of polarised and unpolarised light is incident on a polariser As the polariser is rotated through 360 it is found that the minimum and the maximum of the transmitted intensity is in the ratio 1 q The ratio of intensities of polarised to unpolarised light in the incident beam is A q 1 1 B 1 q 1 C q 1 D 1 q

A thin film of soap solution s 1 4 lies on the top of a glass plate Hg 1 5 When visible light is incident almost normal to the plate two adjacent reflection maxima are observed at two wavelengths 420 and 630 nm The minimum thickness of the soap solution is 420 nm 450 nm 630 nm 1260 nm

a 124 D 8 Fig 2 105 2y z 2D b 3d 24d C d D D 81 In YDSE if a bichromatic light having wavelengths A am A is used then the maxima due to both lights will overlap a certain distance y of from the central maxima Tai separation between slits as d and distance between scree and slits as D Then the value of y will be 6d D b 2 22 x 2d D

Paragraph for In a modified Young s double slit experiment there are three identical parallel slits S S and S A coherent monochromatic beam of wavelength 700 nm having plane wavefronts falls on the slits The intensity of the central point O on the screen is found to be 1 W m The distance S S S S 0 7 mm and screen is 30 cm from slits 0 Find the intensity on the screen at O if S and S are covered g 12 A 17 A Find the intensity on the screen at O if only S is covered 31 7 0 B 31 C 7 Io 6 310 D D To All three slits are now uncovered and a transparent plate of thickness 1 4 am and refractive index 1 25 is placed in front of S Rresultant intensity at point O is 31 7 C 4 1 7 D 5 1 7 D 6 1 7

Plane wavefronts are incident on a glass slab which has refractive index as a function of distance Z according to the relation 1 Z Z This glass slab can acts as lens of focal length F By using the concept of optical path length calculate the focal length of the slab Consider t and z to be very small as compared to F A Z 2 t C Z 2t B Z t D None 2 Z

In Young s double slit experiment the 10th maximum of wavelength A is at a distance of y from the central maximum When the wavelength of the source is changed to 2 5th maximum is at a distance of y2 from its 11 2 central maximum The ratio Y2 is Question Type Single Correct Type 1 2 3 2X 1 242 X X 2X2

4 In a Young s double slit experiment the angular position 0 of a bright fringe having intensity one forth of the maximum intensity is given by YEL u a sin c sin 1 2 4d 2 2d 50 max max b sin d sin 1 2 3d odi Cur

75 M and M are plane mirrors and kept parallel to each other At point O there will be a maxima for wavelength A Light from a monochromatic source S of wavelength A is not reaching directly on the screen Then is M a 3d2 D 472 S d M D Fig 2 102 b

Q 17 Consider a usual set up of Young s double slit experiment with slits of equal intensity moitos as shown in the figure Take O as origin and the Y axis as indicated If average intensity eonatalb AD Isnottoa AD between y and y2 4d equals n 4d let times the intensity of maximum then n equal is take average over phase difference inic irli hiS S A Ke S D O

An object is placed in front of a spherical mirror 18 whose 2 times magnified image is formed on screen Then choose CORRECT option 1 Mirror is concave m 2 2 Mirror is concave m 2 3 Mirror is convex m 2 4 Mirror is convex m 2 An atomic power nuclear reactor can deliver 19 for fund een aantan gerat af ufafa 1 m 2 2 Sade m 2 3 m 2 4 2 300 MW au avut

A thin equiconvex lens has focal length 10 cm and refractive index 1 5 One of its faces is now silvered and for an object placed at a distance u in front of it the image coincides with the object The value of u is Question Type Single Correct Type 1 2 3 4 10 cm 5 cm 20 cm 15 cm

40 A Narrow cylindrical beam of light falls on a spherical air bubble located in a liquid so that the axis of the beam passes through the center of the bubble Determine the refractive index of the liquid if it is known that the area of the beam at the exit from the bubble is 4 times the cross sectional area at the entrance C 2 A 1 5 B 4 3 D 1 75

5 4 the fringe width will remain unchanged In single slit pattern intensities at angul 0 are I 77 2a 37 position 0 0 57 2a and I respectively then 1 I I L 3 L I L 2 4 1 L 4 L L L

3 In YDSE set up two thin transparent slabs of same refractive index having thickness t and 3t are introduced in front of slits as shown in figure As a result the first order minimum is formed at central point O then value of 2 is 1 pt 3 3 1 t 0 2 4 1 4 4 t servo RECHEIOUND DEM ERSTEN

In the diffraction from a single slit of width 2 5 the total number of minimas and secondary maximum maxima on either side of the central maximum are A B C D 4 minimas 2 secondary maximas 2 minimas 2 secondary maximas 2 minimas 4 secondary maximas 2 minimas 3 secondary maximas h

Two coherent light sources S and S A 6000A are 1mm apart from each other The screen is places at a distance of 25 cm from the sources The width of the fringes on the screen should be A skipped B C D 0 015 cm 0 013 cm 0 01 cm 0 10 cm

monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation If the refractive index of the material of the prism is 5 then the angle of incidence is 90 O 30 O 45 60

A rectangular cavity ABCD is carved inside an equilateral prism PQR of refractive index 2 shown in the figure For a ray entering at face PQ and emerging at face PR without passing through AB and CD 53 R there will not be any effect of cavity on 8 B there may be any effect of cavity on 8 for cavity filled with water 8min 30 for cavity filled with air 8min 30 I

1 Two slits are 1 mm apart and the screen is placed one metre away Source produces blue and yellow light which is placed symmetrically with respect to slits to obtain interference on the screen Find position on screen from central bright where maxima of both colours coincide wavelength of blue colour is 480 nm and wavelength of yellow colour is 540 nm 1 3 84 mm 2 4 32 mm

28 In single slit diffraction the width of slit and wavelength used is A Find angu separation between 3 dark fringes above below central maxima The distance of scr from slit is D 1 32 b 2 b 3 3XD 67 B

A ray of light is refracted through a transparent sphere of refractive index n 2 in such a way that it passes through the extremities of two radii which make an angle 8 90 with each other If is the deviation of the ray caused by the sphere then value of is 45 90 60 30

Young double slit experiment is performed in air At certain position 3rd minima is found If same arrangement is placed in a liquid then 3rd maxima is found at that position The refractive index of the liquid is e

In Young s double slit experiment with light of wavelength 600 nm intensity of central fringe is I Now one of the slit is covered by glass plate of refractive index 1 4 and thickness t 5 m the new intensity at the same point on screen will be 31 1 24 24 0 1 1 14 2 3 L

1 2 3 refraction In Column I the parallel rays are incident o some optical device and in Column II the shap of emergent wavefronts are shown Seled incorrect match Column I Column II x

The superposition takes place between two waves of frequency f and amplitude a The maximum intensity Imax Constant x Then x will b 0 2a 2a Marks 4a

In Young s double slit experiment d D 10 4 d distance between slits D distance of screen from the slits At a point P on the screen the resulting intensity is equal to the intensity due to individual slit Io Then the distance of point P from the central maximum is 6000 Question Type Single Correct Type 1 2 mm 2 1 mm 3 0 5 mm

14 In a young double slit apparatus the screen is rotated by 60 about an axis parallel to the slits The slits separation is 3 mm slit um to screen distance at central fringe is 4 m and wavelength of light is 450 nm The separation between the third dark fringe on the either side of central fringe is 1 6 mm 3 4 3 mm 2 8 mm 4 2 3 mm

A hemispherical surface of radius R and refractive index 1 5 is polished as shown At what distance x from point P a point object Obe placed so that its image coincides with the object itself X 1 5 R 02R O 3 R P R

Two coherent sources S and S are placed at small separation One of the two sources is moved in a line perpendicular to the line joining the initial position of sources The equation of locus of zero order maxima of the interference is a variable straight line which is always tangent to a fixed curve in x y plane Find the equation of locus of point of contact with the fixed curve and above mentioned variable straight line STO 1 42x 82 S 42 0 2 x A X y 2 4 x y v2 2 22

ILLUSTRation 3 9 Two sources are placed on x axis at a separation d 32 An observer starts moving from A on a circular track of radius R R d How many bright points and dark points will he observe Find the angular positions of maxima and minima C B R S K S D

In an elliptically polarised light the amplitude of the vibrations a remains constant b changes in direction only c changes in magnitude only d both b and c 199

A man of height 3 2 m wants to see himself in plane mirror from top to bottom The plane 3 mirror is inclined with vertical wall at angle 53 If the least size of mirror to see him is m the distance of eve from mirror is d 3m n

21 The refractive index of a thin film is 1 42 If it is illuminated by sodium light 2 5 9x107 meter find the minimum thickness of the film to be appear black in reflected light A 2 07X10 meter B 2 07X10 meter C 2 07X10 meter D 2 07X10 meter DO DO

A particle of mass 1 ug is dropped from height 20m Its de Broglic wavelength is 1 3 3 x 10 kg m s 2 3 3 x 10 kg m s 3 6 6 x 10 kg m s

3 In Young s experiment using monochromatic light the fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index 1 6 and thickness 2 micron is introduced in the path of one of the interfering waves The mica sheet is then removed and the distance between the slits and the screen is doubled It is found that the distance between successive maxima now is the same as the observed fringe shift upon the introduction of the mica sheet The wavelength of light is A