Optics Question 140

Question: In Young’s double slit experiment, white light is used. The separation between the slits is b. The screen is at a distance d (d» b) from the slits. Some wavelengths are missing exactly in front of one slit. These wavelengths are

[IIT 1984; AIIMS 1995]

Options:

A) λ=b2d

B) λ=2b2d

C) λ=b23d

D) λ=2b23d

Show Answer

Answer:

Correct Answer: A

Solution:

Path difference between the rays reaching infront of slit S1 is. S1PS2P=(b2+d2)1/2d For distructive interference at P S1PS2P=(2n1)λ2 i.e., (b2+d2)1/2d=(2n1)λ2

d(1+b2d2)1/2d=(2n1)λ2

d(1+b22d2+)d=(2n1)λ2 (Binomial Expansion)

b2d=(2n1)λ2λ=b2(2n1)d For n=1, 2, λ=b2d, b23d



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