In a Young's double slit experiment, an angular width of the fringe is 0.35° on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is 1/α. The value of α is ___________.

Solution

Physics sir · 3 steps

In the medium only the wavelength changes: it shrinks by μ, so the angular width shrinks by μ too.

1. Angular width formula. The angular width of a fringe is θ = λ/d. It depends only on the wavelength and the slit separation, not on the 2 m screen distance.
2. Effect of the medium. Immersing the whole set-up leaves d unchanged. Inside the medium the wavelength becomes λ' = λ/μ, so the angular width becomes θ' = θ/μ.

   θ' = θ/μ = 0.35°/(7/5) = (0.35 × 5)/7 ° = 0.25° = 1/4 °

3. So. The new angular width is 1/4 degree, which matches 1/α, so α = 4.

The idea to keep. In YDSE, a medium of refractive index μ divides the wavelength by μ. Angular width, fringe width and fringe angles all shrink by the same factor μ.

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