In a Young's double slit experiment two slits are separated by 2 mm and the screen is placed one meter away. When a light of wavelength 500 nm is used, the fringe separation will be :

Solution

Physics sir · 4 steps

Fringe width is just λ D/d. Put everything in metres first and the answer falls out.

1. Fringe width formula. In YDSE the distance between two neighbouring bright fringes depends on the wavelength λ, the slit-to-screen distance D and the slit separation d.

   β = (λ D)/d

2. Convert to metres. λ = 500 nm = 5 × 10⁻⁷ m, D = 1 m and d = 2 mm = 2 × 10⁻³ m.
3. Put in numbers. β = (5 × 10⁻⁷ × 1)/(2 × 10⁻³) = 2.5 × 10⁻⁴ m.
4. So. β = 0.25 mm, which is option (b).

The idea to keep. Fringe width β = λ D/d grows with wavelength and screen distance and shrinks as the slits move apart. Convert every length to metres before you divide.

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