Question

Laser light of wavelength lambda passes through a thin slit of width a and produces its first dark fringes at angles of +/- 30 degree with the original direction of the beam. The slit is then reduced in size to a circle of diameter a. When the same laser light is passed through the circle, the first dark fringe occurs at:________

A) +/- 66.9 degree.
B) +/- 45.0 degree.
C) +/- 37.6 degree.
D) +/- 36.6 degree.
E) +/- 15.0 degree.

Answer 1

D) θ₂= 36. 6º

Step-by-step explanation:

In this diffraction experiment it is described by the equation

sin θ = m λ

The first dark strip occurs for m = 1 and since the angle is generally small we can approximate sine to the value of the angle

θ₁ = λ/ a

This equation is valid for linear slits, in the case of a circular slit the problem must be solved in polar coordinates, so the equation changes slightly

θ₂ = 1.22 λ / a

In the proposed exercise we start with a linear slit of width a, where tes1 = 30º and end with a circular slit of the same diameter

θ₂ = 1.22 λ / a

Let's clear (Lam/a) of equalizing the two equations

θ₁ = θ₂/ 1.22

θ₂ = 1.22 θ₁

θ₂ = 1.22 30

θ₂= 36. 6º

When reviewing the correct results is D