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Q.Fraunhofer diffraction by a single slit is produced on a screen by using light of wavelength 600 nm. The width of the central maximum is 1 mm. If the wavelength of light is changed to 400 nm, the width of the central maximum will be

(a) 0.5 mm
(b) 0.66 mm
(c) 1 mm
(d) 1.5 mm
Odisha ChseOdisha CHSE +2 Science Board Exam 2018MCQ· 1mImportance★★★★★
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Central-maximum width is proportional to wavelength: W' = W x (lambda'/lambda) = 1 x (400/600) = 0.66 mm, option (b).

In single-slit Fraunhofer diffraction the first minima lie at sin⁡θ=±λ/a\sin\theta = \pm\lambda/a, so the angular width of the central maximum is 2λ/a2\lambda/a and its linear width on a screen at distance D is

W=2λDaW = \dfrac{2\lambda D}{a}

Step 1 — For a fixed slit width aa and screen distance DD, W∝λW \propto \lambda.

Step 2 — Form the ratio for the two wavelengths: …

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