In a Young’s double slit experiment, light of 500 nm is used to produce an interference pattern. When the distance between the slits is 0.05 mm, the angular width (in degree) of the fringes formed on the distance screen is close to

Solution

Physics sir · 4 steps

Angular fringe width is just λ over d, and it comes out in radians, so convert at the end.

1. Angular width formula. Fringe width on the screen is β = (λ D)/d. Dividing by the screen distance D gives the angle one fringe subtends at the slits, so D drops out.

   θ = β/D = λ/d

2. Put in numbers. With λ = 500 × 10⁻⁹ m and d = 0.05 × 10⁻³ m = 5 × 10⁻⁵ m, θ = (5 × 10⁻⁷)/(5 × 10⁻⁵) = 0.01 rad.
3. Convert to degrees. One radian is 180/π ≈ 57.3°, so θ = 0.01 × 57.3° ≈ 0.573°.
4. So. The angular width of the fringes is close to 0.57°, option (c).

The idea to keep. Angular fringe width λ/d does not depend on the screen distance. The formula always gives radians, so multiply by 180/π ≈ 57.3 when the answer is asked in degrees.

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