Question

What is the radius of the central bright spot resulting from illuminating a circular aperture of diameter 0.5 mm with a laser having a wavelength of 500 nm? The screen is 82 cm from the aperture. Choose the closest. a) 1 nm b) 1

Answer 1

Hi, I have used the information given in Hyperpysics to solve this problem. I am attaching the screenshot of the page.

The distance of first minima from centre will give the radius of of the central bright spot.
Now, D = 82 cm = 0.82m, d = 0.5 mm = 0.5 x 10^-3 m, $\lambda=500 nm$ , m = 1.220

So,

$Radius = D\frac{m \lambda}{d} = 0.82 \times \frac{1.220 \times 500 \times 10^{-9}}{0.5 \times 10^{-3}}=1.0004 \times 10^{-3}m=1mm$

Option: C

Answer 2

The angle, A, between the axis and 1st dark fringe is given by sinA=1.22lambda /d (d = aperture diameter;

sinA=1.22*500*10^-9/0.0005

=1220000*10^-9

=0.122

A=7.16 degree

For small angles tanA = sinA to a good approximation
R = DtanA = DsinA = D x 1.22lambda/d

=0.122/0.82

=0.149m