Wave Optics Questions and Answers

A parallel beam of monochromatic light falls normally on a narrow slit of width a to produce a diffraction pattern on the screen placed parallel to the plane of the slit Use Huygens principle to explain that i the central bright maxima is twice as wide as the other maxima ii the intensity falls as we move to successive maxima away from the oither side Delhi 2014C

length 15 cm is cut into two equal halves as shown in Fig 9 72 What is the focal length of each half CBSE Sample Paper 98 Solution For the equiconvex lens let R R R R Then from lens maker s formula 1 7 1 1 2 R R 1 R For each half lens R R R 00 1 1 1 7 7 1 Dividing i by ii we get f 2 1 R spol Fig 9 72 1 R 2 leapt 1 ii

A thin convex lens L refractive index 1 5 is placed on a plane mirror M When a pin is placed at A such that OA 18 cm its real inverted image is formed at A itself as shown in figure When a liquid of M 777777 refractive index is put between the lens and the mirror the pin has to be moved to A such that OA 27 cm to get its inverted real image at A itself The value of will be 2019 Main 9 April II a 3 4 c 3 b 2 3 2 d A A

is a 28 In a Young s double slit experiment using mono chromatic light the fringe pattern shifts b nig by a certain distance on the screen when a mica sheet of refractive index 1 6 and thickness 1 964 micron is introduced in the path of one of the interfering waves The mica sheet is then removed and the distance between the screen and the slits 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 Calculate the wavelength of the monochromatic light used in the experiment Ans 5900 9 In a Young s double slit experiment 500

If one of the slits of a standard YDSE apparatus is covered by a thin glass slab so that it allows only half of the light intensity of the other then A Resultant intensity at centre of screen will decrease B Resultant intensity at dark fringe will increase C The fringe width will remain unchanged D The fringe pattern will shift on the screen toward the covered slit

In young s experiment the upper slit is covered by a thin glass plate of refractive index and of thickness 97 where is the wavelength of light used in the experiment The 3 2 lower slit is also covered by another glass plate of thickness 2x refractive index shown in figure If I is the intensity at point P due to slits S S each then S 11 dIt S j0 d 0 D d D d as A Intensity at point P is 41 B Two fringes have been shifted in upward direction after insertion of both the glass plates together C Optical path difference between the waves from S S at point P is 27 D If the source S is shifted upwards by a small distance d then the fringe originally at

In a YDSE experiment if a slab whose refractive index can be varied is placed in front of one of the slits then the variation of resultant intensity at mid point of screen with will be best represented by 1 Assume slits of equal width and there is no absorption by slab mid point of screen is the point where waves interfere with zero phase difference in absence of slab a c b d 41 1

7 A point object O is placed in front of a concave mirror of focal length 10 cm A glass slab of refractive index u 3 2 and thickness 6 cm is inserted between object and mirror The position of final image when the distance x is 5 cm as shown in figure is 0 1 15 cm 3 2 cm 6cm 32cm x 2 17 cm 4 13 cm onl

intensity 10 2 B Io 2 D 2 Io C L 2 Light of wavelength 6000 x 100 metre is incident on a slit The first minimum of the diffraction pattern is observed to lie at a distance of 6 mm from the central maximum on a screen placed at distance of 2 metre from the slit Then the width of the slit is A 2 0 cm B 0 2 cm D 0 01 cm 0 02 cm 6 The distance between the first and the sixth minima in the diffraction pattern of a single slit is the slit If the wavelength of light used is 5000 A then

6 Match the corresponding entries of column 1 with column 2 Where m is the magnification produced by the mirror Column 1 Column 2 A m 2 p Convex mirror B m q Concave mirror C m 2 r Real image 1 D m s Virtual image 2 a A p and s B q and r C q and s D q and r A rand s B q and s C q and r D p and s c A q and r B q and r C q and s D p and s d A p and r Bp and s C p and q NEFT I 2016 b 1 2

As shown in the figure a glass prism of refractive index 4 3 is immersed in a liquid of refractive index 5 4 The beam of light incident normally on the face P Q is totally reflected to reach the face QR Find out which of the following statement is correct R 3 A sin B sin C 5 2 15 16 23 sin 0 D None of these 15 16

away from the slits S and S2 In each of these cases S Po S2Po S1P1 S2P1 N 4 and S1P2 S2P2 N3 Column I shows four situations of standard Young s double slit arrangement with the screen placed far where is the wavelength of the light used In the cases B C and D a transparent sheet of refractive index and thickness t is pasted on slit S The thicknesses of the sheets are different in different cases The phase difference between the light waves reaching a point P on the screen from the two slits is denoted by o P and the intensity by 1 P Match each situation given in Column l with the statement s in Column ll valid JEE 2009 8 240 for that situation Column II Column l SI A 5 1 S B 1 t 4 C 1 t 2 1 t 37 4 S S Sz S S S P PPP 0 P S P P Po P P PPP Po P PAIA P at p 8 Po 0 q 8 P 0 r I P 0 s I Po I P t 1 P2 I P1

In Young s double slit experiment the intensity at a point P on the screen is half the maximum intensity in the interference pattern If the wavelength of light used is A and d is the distance between the slits the angular separation between point P and the center of the screen is Asin 4 sin B

A B C D A plane mirror which rotates 10 times per minute reflects light on to a stationary mirror 50 m away This mirror reflects the light normally so that it strikes the rotating mirror again The image observed in the rotating mirror is shifted through 2 4 minutes from the position it occupies When the rotating mirror is stationary what is the speed of light 3 x 10 m s 4 x 10 m s 5 x 108 m s

In Young s double slit experiment white light is used The separation between the slits is kept 1 mm and intensity is observed on screen distance 2m from the plane of the slits At a point on the screen directly opposite to the either slit which of the following wavelength is not present

Interpret Young s Double slit experiment Two straight and narrow parallel slits 3mm apart are illuminated by a monochromatic ligh of wavelength 5900 A Fringes are obtained on a screen 60cm away from the slits Calculate the fringe width

TU YDSE the phase difference between two coherent sources is and constant The intensity at a point whic 3 at equal distance from the sources is 1 is maximum intensity

d Cylindrical mirror he focal length of a concave mirror is f and the distance from the object to the principle focus is x The ratio of the size of the image to the size of the object is Kerala PET 2005 a f b X c f x f F d 1 2

A point source S is placed at the bottom of different layers as shown in the figure The refractive index of bottom most layer is uo The refractive index of any other upper layer is H n Ho where n 1 2 A 4n 18 ray of light with angle i slightly more than 30 starts from the source S Total internal reflection takes place at the upper surface of a layer having n equal to 60

Sodium light of wavelengths 589 nm and 589 6 nm are made incident normally on a grating having 500 lines mm Calculate the angular dispersion of these lines in the spectrum of first order Obtain an expression for numerical aperture of an optical fibre 5 3 2

66 A particle is dropped from a height H The de Broglie wavelength of the particle as a function of height is proportional to NCERT Exemplar b H 2 d H a H 7 The photoelectrin th c Ho

3 Plane waves from a magnesium lamp 2 518 36 nm arrive perpendicularly on an opaque screen containing a long 0 250 mm wide slit A large nearby positive lens forms a sharp image of the Fraunhofer diffraction pattern on a screen The center of the fourth dark fringe is found be 1 20 mm from the central axis Determine the focal length of the lens

The Solar Constant 2 calories per square centimeter per minute is the annual amount of solar energy available at the top of the earth s atmosphere O the solar power density at 93 million miles from the sun the average solar power density at ground level on earth extremely variable 220 More than one of the above statements are true

S Answer S A The wavelength of the light emitted by the sources is A The distance between adjacent sources is d 3A The distance of S from the screen is D X Find the minimum non zero distance x of a point P on the screen at which complete darkness is obtained D d S Your Attempt 2 2D 7 17D Screen X Correct answer Rate this question

In a standard YDSE setup if the screen is kept tilted as shown find the distance OA if first maximum is formed at A Wavelength of light emitted by source is Answer B C Your Attempt D DA sec 0 d tan 0 DA sec 0 d A sin 0 DA cos d A tan 0 Screen Correct answer Rate this ques

9 Which of the following functions for y can never represent a travelling wave a x vt b log c e d x vt Xo A x vt xo 1 X vt 1 Only a 2 b c 3 c d 2

the value of k if FSHM FHM 0 9 for y 0 1 m How are Newton s Rings formed Find the wavelength of light if the diameters of 8th and 1 dark fringes are 4 16 mm and 5 09 mm respectively The radius of curvature is 1000 mm

In Young s double slit experiment 12 fringes are observed to be formed ina certain segment of the screen when light of wave length 600 nm is used If the wavelength of light is changed to 400 nm number fringes observed in the same segment of the screen is given by 1 12 3 24 2 18 4 30

Two identical thin plano convex glass refractive index 1 5 each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre The intervening space is filled with oil of refractive index 1 7 The focal length of the combination is 1 25 cm 3 50 cm 2 50 cm 4 20 cm

Among the two interfering monochromatic sources A and B A is ahead of B in phase the observation be taken from point P such that PB PA 2 4 Then the phase diffe between the waves from A and B reaching P is a 156 b 140 c 136 d 126

Assuming that light of wavelength 550 nm is coming from a star The limit of resolution of a telescope whose objective lens has diameter of 1 22 m is O 2 5 x 10 6 rad O 5 5 x 10 7 rad hr mir O 1 6 10 7 rad

a young s double slit experiment the slits are illuminated by monochromatic light The entire set up is immersed in pure water In order to restore the original fringe width what can be done The slits can be brought closed together The screen can be moved away from the slit plane The incident light can be replaced by that of a longer wavelength A thin transparent slab can be introduced in front of one of the slits

In a Young s double slit experiment slits are separated by 0 5 mm and the screen is placed 150 cm away A beam of light consisting of two wavelengths 650 nm and 520 nm is used to obtain interference fringes on the screen The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is 2017 Main a 7 8 mm b 9 75 mm c 15 6 mm d 1 56 mm

1 Violet light is falling on a photosensitive material causing ejection of photoelectrons with maximum kinetic energy of 1 eV Red light falling on metal will cause emission of photoelectrons with maximum kinetic energy approximately equal to 1 1 2 eV 2 0 9 eV 3 0 5 eV

The maximum intensity of fringes in Young s experiment is 1 If one of the slits is closed then intensity at that place becomes Then relation between I and is

In physics laboratory a student is trying to calculate the focal length of a convex lens He measures the distance between screen and a light source lined up on the optical bench to be 120 cm When he shifts the lens along the axis of optical bench sharp image of source is obtained at two lens positions He also measures the ratio of these two magnifications to be 1 9 Which image as seen by student is brighter smaller O bigger both are equally bright can not be judged

50 In Young s double slit interference experiment if the n bright fringe for light of wavelength 2 n 0 1 2 coincides with the mth dark fringe for light of wavelength 2 m 1 2 3 then the ratio A is a b m 1 n 2m 1 2n c d 2m 1 n 2m 1 2n

A zero 2 cm C 4 cm D 1 cm A person s eye is at a height of 1 5 m He stands infront of a 0 3m long plane mirror which is 0 8 m above the ground The length of the image he sees of himself is A 1 5m B 1 0m C 0 8m D 0 6m wall clock shows time 04 25 37 where 1st term represents hours 2nd represents

7 Two prisms of prism angles A and A are placed in contact with each other with second prism upside down The refractive indices for violet and red colours for their materials are u 1 753 MR 1 751 and 1 758 R 1 754 A white light ray when made to fall upon combination from one side emerges from the other side such that the constituents colour rays are parallel to pach other If A 5 then A

Assuming the Sun to be a spherical body of radius R at a temperature of TK evaluate the total radiant powerd incident of Earth at a distance r from the Sun 2 a 4 r R 0 T4 2 r c R 6 TOR 0 T4 2 4 r 2 T4 b R 0 T4 d R T 2

25 White coherent light 400 nm 700 nm is sent through the slits of a Young s double slit experiment figure 17 E3 The separation between the slits is 0 5 mm and the screen is 50 cm away from the slits There is a hole in the screen at a point 1 0 mm away along the width of the fringes from the central line a Which wavelength s will be absent in the light coming from the hole b which wavelength s will have a strong intensity T 0 5 mm 50 cm Figure 17 52 1 0 mm

20 Ratio of width of principal maxima to the second order maxima in Fraunhofer single slit diffrac 1 4 3 2 2 3 4 1

In a biprism experiment by using light of wavelength 5000 A 5 mm wide fringes are obtained on a screen 1 0 m away from the coherent sources The separation between the two coherent sources is MP PMT PET 1998 b 0 1 mm d 0 01 mm a 1 0 mm c 0 05 mm

c 0 1 cm In Young s double slit experiment the distance between sources is 1 mm and distance between the screen and source is 1 m If the fringe width on the screen is 0 06 cm then CPMT 1996 a 6000 A c 1200 b 4000 d 2400

A plane wavefront wavelength 2 is falling on YDSE apparatus as shown in the figure The lower half of it is filled with water refractive index 1 5 How many maximas can be theoretically obtained on the screen if d 98 and D 20000 A including the maxima at infinity A 245 C 122 B 246 D 123 404

In Young s experiment the distance between the slits is reduced to half and the distance between the slit and screen is doubled then the fringe width IIT 1981 MP PMT 1994 RPMT 1997 KCET 2000 CPMT 2003 AMU Engg 2000 DPMT 2003 UPSEAT 2000 04 Kerala PMT 2004 b Will become half d Will become four times a Will not change c Will be doubled

Two point monochromatic and coherent sources of light of wavelength 2 are placed on the dotted line in front of an infinite screen The sources emit waves in phase with each other The distance between S and S is d while their distance from the screen is much larger A If d is B Ifd is 32 D If dis 11 6 C If d is 32 then O will be maxima S at O minima will be observed 2 72 6 then intensity at O will be S the intensity at O will be 3th 4 3th 4 O of maximum intensity of maximum intensity

For Problems 10 12 A point source Semits light of wavelength 600 nm It is placed at a very small distance from a flat reflecting mirror AB Interface fringes as observed on the screen placed parallel to reflecting surface at very large distance D from it The ratio of minimum to maximum intensities in the interference fringes formed near the point P is 1 6 A B a elliptical c circular S D Po Screen 10 What is the shape of interference fringes on the screen b paraboloid d none of these 11 What is the percentage intensity of the reflected light to the intensity of the reflected light to the intensity of incident light a 49 b 64 c 81 d 36 12 If the intensity of P corresponds to a maximum calculate the minimum distance through which the reflecting surface AR should be shifted so that intensity at P again becomes

1 101 1 D d S Ko A thin transparent plate is placed on the path of one interfering beam as shown What is the shift in central bright fringe t is thickness of the plate and u refractive index uDt Lo S Po 2 1 tD D

A lens of diameter 5 0 cm and focal length f 25 0 cm was cut along the diameter into two identical halves In the process the layer of the lens a 1 00 mm in thickness was lost Then the halves were put together to form a composite lens In it s focal plane a narrow slit was placed emitting monochromatic light with wavelength 0 60 um Behind the lens a screen was located at a distance b 50 cm from it Find number of possible maxima