A monochromatic parallel beam of light of wavelength λ is incident normally on the plane containing slits S 1 and S 2 . 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 perpendicular to x-axis as shown. The distance between slits is d and that between screen and slit is D. Match the statements in column- Ι with results in column- ΙΙ . (S 1 S 2 << D and λ << S 1 S 2 )
Column- I Column- II
having equal intensities, such that intensity at those points is 
th of maximum intensity.
having equal intensities, such that intensity at those points is 
th of maximum intensity.
having equal intensities, such that intensity at those points is 
th of maximum intensity.
having equal intensities, such that intensity at those points is 
th of maximum intensity.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
( a )→ q,r,s ; → p,q,r,s ; → q,r,s ; → p,q,r,s
Sol. Initially at a distance x from central maxima on screen is
Ι = Ι 0 + 4 Ι 0 + 
cos 
, where β = 
Ι max = 9 Ι 0 and Ι min = Ι 0
At points where intensity is 
th of maximum intensity, minima is formed
∴ Distance between such points is β , 2 β , 3 β , 4 β , .....
At points where intensity is 
th of maximum intensity, cos 
= – 
or x = 
.
∴ Distance between such points is 
, β , β + 
, β + , 2 β , .....
cos 
= 0 or x = 
.
∴ Distance between such points is , β , β + 
, 2 β , .....
cos 
= 
or x = 
.
∴ Distance between such points is , 
β , β + , β + 
, 2 β , .....
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