The centers of two slits of width a are a distance d apart.If the fourth minimum of the interference pattern occurs at the location of the first minimum of the diffraction pattern for light of wavelength λ,the ratio a/d is equal to
A)0.
B) .
C) .
D) .
E) .

Question

The centers of two slits of width a are a distance d apart.If the fourth minimum of the interference pattern occurs at the location of the first minimum of the diffraction pattern for light of wavelength λ,the ratio a/d is equal to
A)0. 
B) . 
C) . 
D) . 
E) .

Quizplus · Accepted Answer

The distance between the centers of the two slits is given as d. The distance between the first minimum of the diffraction pattern and the fourth minimum of the interference pattern is half the distance between two consecutive minima. Thus,

d sin θ = 2λ (For first minimum in diffraction pattern)
d sin θ = (4n-2)λ (For fourth minimum in interference pattern)

where n is an integer greater than or equal to 1.

Dividing the second equation by the first, we get:

2n-1 = 2a/d

or, a/d = (2n-1)/2

For n=2, we get:

a/d = 1

Therefore, the ratio a/d is equal to 1, which can be expressed as 11ea7ff9_2c59_857b_a768_155cf21102cd_TB2295_11 in hexadecimal. Thus, the correct answer is option C.

The Centers of Two Slits of Width a Are a Distance