The angular width Δθ of the central maximum in the diffraction pattern of a slit illuminated by light of wavelength 500 nm is measured. The angular width of the central maximum is found to increases by 25% when the same slit is illuminated by another light of wavelength λ' wavelength λ' (in nm) is

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The angular width Δθ of the central maximum in the diffraction pattern of a slit illuminated by light of wavelength 500 nm is measured. The angular width of the central maximum is found to increases by 25% when the same slit is illuminated by another light of wavelength λ' wavelength λ' (in nm) is

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575

450

375

625

answer is D.

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Detailed Solution

$Δθ = \frac{2 λ}{a}, Δθ' = \frac{2 λ'}{a}$
Given ${Δθ}^{1} = Δθ + 25 % of Δθ$
$\begin{array}{l} = Δθ + \frac{25}{100} Δθ = 1 .25 Δθ \\ ∴ \frac{λ'}{λ} = \frac{Δθ}{Δθ} = 1 .25 \\ \Rightarrow λ' = 1 .25 λ = 1 .25 \times 500 nm = 625 nm \end{array}$