Wave Optics Questions and Answers

31 In a Young s double slit set up light from a laser source falls on a pair of very narrow slits separated by 1 0 micrometer and bright fringes separated by 1 0 millimeter are observed on a distant screen If the frequency of the laser light is doubled what will be the separation of the bright fringes a 0 25 mm c 1 0 mm b 0 5 mm d 2 0 mm

Angular width of a central max is 300 when the slit is illuminated by light of wavelength 6000 Then width of the slit will be approx a 12 x 10 m c 12 x 10 8 m b 12 x 10 7 m d 12 x 10 m

Plane sound waves of wavelength 0 12 m are incident on two narrow slits in a box with non reflecting walls as shown At a distance of 5 0 m from the center of the slits a first order maximum occurs at point P which is 3 0 m from the central maximum The distance between the slits is most nearly 0 07m 0 09m 0 16m 0 20m Sound A 0 12m 19 SP 13 0 m

Draw the graph showing intensity distribution of fringes with phase angle due to diffraction through single slit OR What should be the width of each slit to obtain n maxima of double slit pattern within the central maxima of single slit pattern 2

5 A parallel beam of light 2 5890 A is incident on thin glass plate u 1 5 such that the abgle of refraction into the plate is 60 Calculate the smallest thickness of the glass plate which will appear dark by reflection Ans 3 926x10 5 cm

4 In Young s double slit experiment the slits are 0 5 mm apart and interference is observed on a screen placed at a distance of 100 cm from the slits It is found that the 9th bright fringe is at a distance of 8 135 mm from the dark fringe from the center pattern Find the wavelength of light used Ans 5890 A

distance between two fringes from center Ans 2 One slit in Young s double slit experiment is wider than the other so that the amplitude of the light reaching the center point on the screen from one slit acting alone is twice that of the other slit acting 10 alone Find the expression for the resultant intensity I at on the screen Ans 1 8cos 2d sin 8

wavelength in the visible region will be reflected most strongly Ans 5230 A In Newton s rings experiment the diameter of the 4th and 12th dark rings are 0 400 cm and 0 700 cm respectively Find the diameter of the 20th dark ring Ans 0 906 cm 0 Light containing two wavelengths 2 and 2 falls normally on a planoconvey lens of radius of

Light containing two wavelengths 1 and 22 falls normally on a planoconvex lens of radius of curvature R resting on a glass plate If the nth dark ring due to 21 coincides with the n 1 th dark ring due to 22 prove that the radius of nth dark ring of 21 is 1 R 1 1

In Young s double slit experiment a thin transparent sheet of thickness t and refractive index is introduced in the path of one of the interfering beams This shifts the entire fringe system through a constant distance Now estimate the thickness of the sheet if the fringe system displacement is S Assume that the distance between slits is 2d distance between slits and screen is D Ans t D 1 2Sd

ir at a ooking 4 1 75 D uld the beyond 6 The following diagram shows a glass sphere of radius 10 em with a paraxial incident ray The refractive index of the material of the glass is 1 2 2 1 5

In a YDSE a parallel beam of light of wavelength 6000A is incident on slits at angle of incidence 30 A and B are two thin transparent films each of refractive index 1 5 Thickness of A is 20 4 m Light coming through A and B have intensities I and 41 respectively on the screen Intensity at point O which is symmetric relative to the slits is 31 The central maxima is above O i What is the maximum thickness of B to do so Assuming thickness of B to be that found in part i answer the following parts ii Find fringe width maximum intensity and minimum intensity on screen iii Distance of nearest minima from O iv Intensity at 5 cm on either side of O 30 IB 10 1mm 1m

For a transparent and permittivity medium relative permeability fr Mr and E are 1 0 and 1 44 The velocity of light in this medium respectively would be A 4 32 108 m s B 2 5 x 108 m s C 3 108 m s D 2 08 108 m s

Width of face of a person is 18 cm He is looking at his face if separation between the eyes is 8 cm What is the minimum width of mirror required see face B 5 cm 4 cm 10 cm 9 cm Correct Answe My Answe

A trihedral prism with refracting angle 60 deviates a light ray by 30 The refractive index of the material of prism Question Type Multiple Correct Type 1 may be equal to 2 2 3 4 can not be greater than 2 can not be less than 2 none of these

Two ideal slits S and S are at a distance d apart and illuminated by light of wavelength passing through an ideal source slit S placed on the line through S2 as shown The distance between the planes of slits and the source slit is D A screen is held at a distance D from the plane of the slits The minimum value of d for which there is darkness at O is S S S DD 3XD 2 1 2 VAD 3 XD 4 3XD 0

In a double slit experiment a monochromatic light of wavelength 500 nm is used The fringe pattern is observed on a screen 1m away on a screen Fringe width is found to 0 4mm If the entire arrangement is immersed in a liqid in which velocity of light is 1 5 x 108 ms 1 then the fringe width becomes A 0 2 mm B 0 3 mm C 0 4 mm D 0 25 mm

Question 24 1a A pair of slits separated by 1 75 x 10 4 m is illuminated by 594 nm light and an interference pattern is observed on a screen 2 35 m from the slits Determine the difference in path lengths from each of the slits to the following locations a to the location of a second order bright fringe on the screen um b to the location of a second dark fringe on the screen relative to the central maximum m

Q 13 O Moderate A leaf which contains only green pigments is illuminated by a laser light of wavelength 0 632 m It would appear to be Brown Black Red 00 14

What is the approximate radius of the central bright diffraction spot of light of wavelength 0 5 m if focal length of the lens is 20cm and radius of aperture of the lens is 5cm 1 1 22 m 3 4 22 m 2 2 30 m 4 6 23 m

maximum et rays are 26 The average energy density of electromagnetic wav given by E 50 N C sin wt ke will be nearly 1 10 8 J m 2 10 7J m 3 10 J m 4 10 5 J m

The focal lengths of a lens for violet green and red light rays are fy fg and fa respectively Which of t relationship A fR fG fy fy fG fR fG fR fy fc fy fr

In a Fraunhofer diffraction experiment at a single slit using a light of wavelength 400 nm the first minimum is formed at an angle of 30 The direction of the first secondary maximum is given by O sin sin 3 3 4

Two slits S and S lie on the x axis and symmetric with respect to y axis are illuminated by a parallel monochromatic light beam of wavelength I as shown The distance between slits is d X Point O is the mid point of the line S S and this point is considered as the origin The slits are in horizontal plane The interference pattern is observed on a horizontal plate acting as screen of mass m which is connected to one end of a vertical massless spring of spring constant k The other end of the spring fixed to ground At t 0 the plate is at a distance D d below the plane of slits and spring is in its natural length The plate is released from rest from its initial position The rate by which fringe width will increase when acceleration of plate is zero is plate S O eeeeeee 41 Hx S k m

an incident plane wavefront makes angle 53 with surface of medium in air The refracted wavefront makes angle 37 w cefractive index of medium is A B U 3 2 4 3 3 4 2 3

In the Young s double slit experiment a mica slip of thickness t and refractive index is introduced in the ray from first H sources By how much distance fringes pattern will be displaced O O 1 4 11 Pu 1t

Q 1 4 1 00 21 A beam of ordinary unpolarised light passes through a tourmaline crystal C and then it passes through another tourmaline crystal C which is oriented such that its principal plane is parallel to that of C The intensity if emergent light isl Now C is rotated by 60 about the ray The emergent ray will have an intensity

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 is the distance between the two first order minima O 1 1mm O 2 1mm O 0 01 mm O 0 1 mm

In the Young s double slit experiment the ratio of intensities of bright and dark fringes is 9 This means that 1 The intensities of individual sources are 5 and 4 units respectively 2 The intensities of individual sources are 4 and 1 units respectively 3 The ratio of their amplitudes is 3 4 The ratio of their amplitudes is 6

Q 7 Moderate 4 1 00 16 The extreme wavelengths of Paschen series are 0 365 m and 0 565 m

Q7 Unpolarized light with an intensity of I is incident on a polarizer The polarizer has its transmission axis aligned at 60 intensity of the light when it emerges from the polarizer O A 1 4 B 21 O C 1 2 D I

In YDSE a laser light is used to illuminate the closely spaced slits as a result a clear interference pattern is obtained on screen If we place smoke particles between the double slit and the screen then the effects of interference will be observed

3 An object shaped as L is placed between two parallel plane mirrors as shown In the first seven closest images how many laterally inverted images are formed 1 1 2 2 3 3 4 4 A plane mirror is placed horizontally on level ground at a distance of 60 m from the foot of a tower Light louiation of 90 The height of the to C

In a Young s double slit experiment with slit separation 0 1 mm one observes a bright 1 40 fringe at angle rad by using light of wavelength X When the light of wavelength 2 is used a bright fringe is seen at the same angle in the same set up Given that X and 2 are in visible range 380 nm to 740 nm their values are

Two sources give interterence pattern which is observed on a screen placed at a distance D from the sources The fringe width is given as 2W If the distance of sources from the screen is doubled then the fringe width will

28 In the figure shown three slits S1 S2 and s3 are illuminated with light of wavelength 2 d and D d Each slit produced same intensity I on the screen If intensity at the point on screen directly infront of s2 is 31 then the maximum value of is nd Find value of n 2D P P S S SS S P

1 An equi convex lens of focal length 10 cm at t 0 and refractive index u 1 5 is placed in a liquid whose refractive index varies with time as t 1 1 0 t If the lens was placed in the liquid at t 0 10 after what time in sec lens will act as concave lens of focal length 20 cm ANSWER

33 60 Mirror 2 1309 1 60 3 0 TI Mirror 1 A ray of light is incident on the surface of mirror I as shown in the figure then what will be the angle of refraction when the light ray passes through the 3 glass slab Refractive index of glass 2 2 90 4 30 Glass Slab 31

In Newton s ring experiment the diameter of the nth dark ring is 8 mm and that of the n 5 th dark ring is 12 mm If the radius of curvature of the plano convex lens is 10 m find the wave length of the light used

Example 9 6 Light from a point source in air falls on a spherical glass surface n 1 5 and radius of curvature 20 cm The distance of the light source from the glass surface is 100 cm At what position the image is formed

a 55 A container made of glass 1 5 contains liquid A ray of light passing through the liquid falls on the bottom of the container at an angle of incidence 0 tan 0 9 and completely polarized The ray should strike the bottom of the container at an angle of incidences so that it undergoes total internal reflection 1 tan 1 5 3 tan 0 75 2 sin 0 9 4 sin 0 45

Coherent light rays of wavelength A strike a pair of slits separated by distance d at an angle 0 as shown in Figure P37 14 Assume an interference maximum is formed at an angle 02 a great distance from the slits Show that d sin02 sin0 mA where mis an integer 8 d Figure P37 14

In YDSE the central bright fringe is at mid point of screen On both side of mid point fringes are obtained Number of fringes on either side is n with air between slits and screen When water 4433 obtained on either side then no is a w is filled n number of fringes are

Find the position coordinates of the image of the object P as seen through the periscope The mirrors are inclined at 45 with x axis and eye is placed at the level y d A d d C 2d d B d d D 3d d A P d d

In a YDSE fringes are observed by using light of 4800 if a glass plate p 1 5 is wavelength introduced in the path of first wave and of same thickness another plate p 1 8 is introduced in the path of the second wave The central fringe takes the position of fifth bright fringe The thickness of plate will be A B C D 8 micron 80 micron 0 8 micron None of these

In Young s double slit experiment when wavelength used is 6000 A and the screen is 40 cm from the slits the fringes are 0 012 cm apart What is the distance in cm between the slits A 0 024 B 24 C 0 24

36 Choose the correct alternative 1 When plane polarised light passes through polaroid it changes its nature to linearly polarised 2 Refracted light when light is incident at Brewster angle is linearly polarised 3 Polarised light can be produced by scatterin through in earth s atmosphere 2 un ic polarised

In a Young s double slit experiment the intensity at the central maximum is lo The intensity at a distance 3 4 from the central maximum is B is fringe width 1 3 lo 2 2 2 4 0 lo 4 Find phone diff

Quest sed on the following write up If Snell s law is found valid for two mediums whose refractive indices have opposite signs the incident and the refracted rays must remain on the same side of the normal at the point of incidence In the figure is shown a ray crossing the interface between two mediums I and II The ray makes angles 0 and with normal in the medium I and II The refractive indices of the mediums and have opposite signs Snell s law is expressed for the above situation as usual by the equation 4 sin 0 sin 0 Therefore to satisfy this equation the angles and must also have opposite signs A self luminous point object placed at a distance x from a slab of transparent material of negative refractive index is viewed through the slab as shown in the figure Thickness of the slab is d refractive index Object of material of the slab with respect to the outside medium is u 1 For different moduli of values of x and d the observer may find real or virtual image of the object Which of the following statements is true a If x d image is virtual and for x d image is real b If x d image is virtual and for x d image is real c If x sd image is virtual and for x d image is real intual and for x d image is real 8 Normal Medium 1 Medium II Slab B Obse

5 A single slit is of width 0 5 mm Distance of screen from slit is 1 m Second maxima in diffraction pattern is at distance 2 mm from centre What is wavelength of light 1 560 nm 3 40 nm 2 400 nm 4 360 nm