Question

Two wavelengths of sodium light of 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture 2 × 10⁻⁶ m. The distance between the slit and the screen is 1·5 m. Calculate the separation between the positions of first maxima of the diffraction pattern obtained in the two cases.

Answer 1

• λ₁ = 590 nm = 590 × 10⁻⁹ m

• λ₂ = 596 nm = 596 × 10⁻⁹ m

• Slit width a = 2 × 10⁻⁶ m

• Distance to screen D = 1.5 m

For λ₁ = 590 × 10⁻⁹:

`y = (1.43lamdaD)/a`

`y_1 = (1.43xx590xx10^-9 xx 1.5)/(2xx10^-6)`

`= (1.43 xx 590 xx 1.5)/2 xx 10^-3`

`= (1.43xx885)/2 xx 10^-3`

`1264.55/2 xx 10^-3 = 632.275  mm`

For λ₂ = 596 × 10⁻⁹:

`y_2 = (1.43 xx 596 xx 10^-9 xx 1.5)/(2 xx 10^-6)`

`= (1.43 xx 596 xx 1.5)/2 xx 10^-3`

`= 1277.22/2 xx 10^-3 = 638.61 xx 10^-3`

= 0.63861m = 638.61mm

Δy = y₂ ​− y₁​ = 638.61 mm − 632.275 mm = 6.335 mm

Separation = 6.34 mm