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

For two slits of width a, the distance between the successive bright fringes is given by:
d(sin θ) = mλ, where m is an integer and d is the distance between the centers of the two slits.

For diffraction through a single slit of width a, the condition for the first minimum is given by:
a(sin θ) = λ

Given that the fourth minimum of the interference pattern occurs at the location of the first minimum of the diffraction pattern, we can equate these two conditions:
4d(sin θ) = a(sin θ)
4d = a

So, the ratio a/d is equal to 4, which can be simplified to 11eb8c7e_f569_518d_8371_050c2fd995f2_TB8847_11. Therefore, the correct answer is C.

The Centers of Two Slits of Width a Are a Distance