Question

Consider a case of single slit diffraction where we are directing a beam of light (of wavelength λ) through a single slit of unknown width “D”. The pattern will be observed on a screen a distance L from the slit. We will be able to take measurements of the pattern on the screen.

Sketch the pattern you would expect to see and derive an expression to relate a characteristic length of the pattern on the screen to the width of the slit.   

Answer 1

In fig (a) there is a slit of width D. Through which beam is directed and it diffracts at an angle θ.

In fig (b) Pattern is formed of bright and dark fringes.

Light passing through a single slit is diffracted in all directions and may interfere constructively or destructively, depending on the angle. The difference in path length for rays from either side of the slit is seen to be L.

Where L = Dsinθ

for destructive(Dark Fringes) interference for a single slit.

Dsinθ = m where m = all integers (1, -1, 2, -2 .....)

and for constructive(Bright fringes) interference for a single slit.

Dsinθ = n/2  where n = all odd integers (1, -1, 3, -3 .....)

where D is the slit width.

is the light’s wavelength.

θ is the angle relative to the original direction of the light, and

m is the order of the minimum.

n is the order of maximum.