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Q.

A monochromatic parallel beam of light of wavelength λ is incident normally on the plane containing slits S1 and S2. The slits are of unequal width such that intensity only due to one slit on screen is four times that only due to the other slit. The screen is placed along y-axis as shown in fig. The distance between slits is d and that between the screen and slits is D. 

Match the statements in Column I with result Column II: 

A monochromatic parallel beam of light of wavelength lambda is incident  normally on the plane containing slits S1 and S2 . The slits are of unequal  width such that intensity only due
 COLUM N-I COLUM N-II
A)The distance between two points on the screen having equal intensities, such that intensity at those points is 1/9 th of maximum intensityP)3d
B)The distance between two points on the screen having equal intensities, such that intensity at those points is 3/9 th of maximum intensityQ)d
C)The distance between two points on the screen having equal intensities, such that intensity at those points is 5/9 th of maximum intensityR)2d
D)The distance between two points on the screen having equal intensities, such that intensity at those points is 7/9 th of maximum intensityS)3d

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a

A-SRQ, B-QRP, C-RPQ, D-PQRS

b

A- QRS, B- QRS, C- PQRS, D- PQRS

c

A- PQRS, B- QRS, C-SRQ, D-RSQ

d

A-QRS, B-PQRS, C-QRS, D-PQRS 

answer is A.

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Detailed Solution

A-QRS, B-PQRS, C-QRS, D-PQRS
Intensity at a distance x from central maxima on screen is I=I0+4I0+2I04I0Cos2πxβ
Where β=d
Imax=9I0 and Imin=I0
a) At points where intensity is (1/ 9)th of maximum intensity, minima is formed. Therefore, distance between such points is β,2β,3β,4β,........
b) At points where intensity is (3/9) th of maximum intensity cos2πxβ=12
Hence distance between such points is β3,2β3,β,β+β3,β+2β3,2β,
c) cos2πxβ=0
Hence distance between such points is β2,β,β+β2,2β,

d) cos2πxβ=12
Hence distance between such points is β3,2β3,β,β+β3,β+2β3,2β,
 

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