Question

The angular separation of the central maximum in the Fraunhofer diffraction pattern is measured. The slit is illuminated by the light of wavelength 6000 Å. If the slit is illuminated by light of another wavelength, the angular separation decreases by 30%. The wavelength of light used is ______.

Options

• 6000 Å

• 3500 Å

• 4200 Å

• 4700 Å

Answer 1

The angular separation of the central maximum in the Fraunhofer diffraction pattern is measured. The slit is illuminated by the light of wavelength 6000 Å. If the slit is illuminated by light of another wavelength, the angular separation decreases by 30%. The wavelength of light used is 4200 Å.

Explanation:

Given, the wavelength of used light, `lambda_1 = 6000` Å

Initial angular separation, β₁ = β

Final angular separation, β₁ = β - 30% of β

β₂ = β - 0.3 β = 0.7 β

We know that, β ∝ λ

⇒ `beta_1/beta_2 = lambda_1/lambda_2`

⇒ `lambda_2 = (beta_2 xx lambda_1)/beta_1 = (0.7beta xx 6000)/beta = 4200` Å