In a single slit diffraction experiment, a light of wavelength 500 nm is used and the second minimum is observed at an angle of 45°. The width of the slit is:

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AAI ATC Junior Executive 27 July 2022 Shift 1 Official Paper

Answer 1

Concept:

In the single-slit diffraction experiment: The bending phenomenon of light or diffraction causes light from a coherent source to interfere with itself and produce a distinctive pattern on the screen called the diffraction pattern.
Diffraction is evident when the sources are small enough that they are relatively the size of the wavelength of light.
Condition for maxima, \(asin\theta = (m+\frac{1}{2})λ\), where m = number of orders, a = slit width, λ = wavelength of the light

Calculation:

Given,

The wavelength of light, λ = 500 nm

The number of orders, m = 2

angle, θ = 45º

The condition for the minima in a single slit diffraction experiment, asinθ = mλ

\(a=\frac{mλ}{sin\theta}\)

\(d=\frac{2\times 500\times 10^{-9}}{sin45}=1.414 ~μ m\)

Hence, the slit width is 1.414 μm

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