A parallel beam of monochromatic light of wavelength 5000 Aᵒ is incident normally on a single narrow slit of width 0.001 mm. The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of _________ (degree).

Solution

Physics sir · 4 steps

First minimum of a single slit: put a sin θ = λ and the sine comes out as exactly one half.

1. Condition for minima. In single slit diffraction, the nth dark fringe appears where a sin θ = nλ. For the first minimum, n = 1. The lens only brings the parallel diffracted rays to a focus on the screen, so it does not change the angle.

   sin θ = λ/a

2. Same units. λ = 5000 Å = 5 × 10⁻⁷ m and a = 0.001 mm = 1 × 10⁻⁶ m.
3. Put in numbers. sin θ = (5 × 10⁻⁷)/(1 × 10⁻⁶) = 0.5.
4. So. θ = sin⁻¹(0.5), so the first minimum is at 30 degrees.

The idea to keep. Single slit minima sit at a sin θ = nλ. The half-wavelength rule belongs to double slit minima. Put a and λ in the same units before dividing.

Answer from the NTA final answer key. Solution by PrepWiser.