Question

Two narrow slits 80 μm apart are illuminated with light of wavelength 640 nm .

What is the angle of the m = 3 bright fringe in radians?

Express your answer using two significant figures.

What is the angle in degrees?

Express your answer using two significant figures.

Answer 1

Given,

separation of the slits, d = 80μm = 80x10^–6m

wavelength of the light, $\lambda$ = 640nm = 640x10^–9m

If the angle of the bright fringe is θ, then we have the relation

sinθ = m$\lambda$/d

Here m is the order of the fringe.

So, for m = 3 bright fringe,

  sinθ = 3x(640x10^–9) / (80x10^–6)

= 3x8x10^–3

= 24x10^–3

sinθ = 0.024

θ = 0.024 radians ($\because$ for small angle, sinθ $\approx$ θ )

So, the angle of m = 3 bright fringe, is 0.024 radians