Optics

The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 µm. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance ? (i.e. distance between the centres of each slit.)

  1. 50 µm
  2. 75 µm
  3. 100 µm
  4. 25 µm

Answer

In diffraction,

d sin 30° = λ

λ = d/2

Let x be the separation between the two slits.

Young's fringe width, β = 1 cm

β = λD/x

10-2 = d/2 × (50×10-2)/x

x = 25 µm

The correct option is D.