Question

A parallel beam of green light of wavelength 546 nm passes through a slit of width 0.4 mm. The intensity pattern of the transmitted light is seen on a screen which is 40 cm away. What is the distance between the two first order minima?

Answer 1

Given : λ = 546 nm = 546 x 10⁻⁹ m, a = 0.4 mm = 4 x 10⁻⁴ m,

D = 40 cm = 40 x 10⁻² m,

y_md = \(m\frac{λD}{a}\)

∴ y_1d = \(1\frac{λD}{a}\)

And 2y_1d = \(2\frac{λD}{a}\)=(\frac{2×546×10^{-9}}{4×10^{-4}}\)

= 2 x 546 x 10⁻⁶ = 1092 x 10⁻⁶

= 1.092 x 10⁻³ = 1.1 mm

This is the distance between the two first order minima.