In a Young's double slit experiment, the slits are separated by 0.2 mm . If the slits separation is increased to 0.4 mm , the percentage change of the fringe width is :

Solution

Physics sir · 3 steps

Fringe width goes as 1/d, so doubling the slit gap halves every fringe.

1. Fringe width formula. In YDSE the fringe width is β = (λ D)/d. Here λ and D stay the same, so β is inversely proportional to the slit separation d.

   β₂/β₁ = d₁/d₂ = (0.2 mm)/(0.4 mm) = 1/2

2. Percentage change. The new fringe width is β₂ = β₁/2. The change is (β₂ - β₁)/β₁ × 100 = -50%, a decrease of 50%.
3. So. The fringe width changes by 50%, so the answer is (b).

The idea to keep. Fringe width β = λ D/d grows with λ and D but shrinks with d. Always take percentage change relative to the original value.

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