Question

In Fraunhoffer diffraction by a narrow slit, a screen is placed at a distance of 2 m from the lens to obtain the diffraction pattern. If the slit width is 0.2 mm and the first minimum is 5 mm on either side of the central maximum, find the wavelength of light.

Answer 1

Given: D = 2 m, y_1d = 5 mm = 5 x 10⁻³ m, a = 0.2 mm = 0.2 x 10⁻³ m = 2 x 10⁻⁴ m

y_md = \(m\frac{λD}{a}\)

∴ λ = \(\frac{y_{1d}a}{D}=\frac{5×10^{-3}×0.2×10^{-3}}{2}\)

∴ λ = 5 x 10⁻⁷ m = 5 x 10⁻⁷ x 10⁻¹⁰ Å = 5000 Å

This is the wavelength of light.