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.

D)  θ₂= 36. 6º  

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

do you have a formula possibly