In a diffraction pattern due to single slit of width ' a ', the first minimum is observed at an angle of 30° when the light of wavelength 5400 is incident on the slit. The first secondary maximum is observed at an angle of (sin 30° = 1/2) (a) sin ⁻¹(3/4) (b) sin ⁻¹(2/3) (c) sin ⁻¹(1/2) (d) sin ⁻¹(1/4)

Answer: (a). First minimum: asin 30° = λ ⇒ a = 2λ. First secondary maximum: asin θ = (3λ)/(2) ⇒ sin θ = 3/4. So the answer is (a) sin ⁻¹(3/4).

In a diffraction pattern due to single slit of width ' a ', the first… | MHT CET 2023 (9 May, Shift 1)

Q47MHT CET 2023 · 9 MAY · SHIFT 1Easy

Diffraction at a Single Slit

In a diffraction pattern due to single slit of width ' $a$ ', the first minimum is observed at an angle of $30^\circ$ when the light of wavelength $5400\text{ \AA}$ is incident on the slit. The first secondary maximum is observed at an angle of $\left(\sin 30^\circ = \frac{1}{2}\right)$

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Answer: (a)

First minimum: $a\sin 30^\circ = \lambda \Rightarrow a = 2\lambda$ .
First secondary maximum: $a\sin\theta = \dfrac{3\lambda}{2} \Rightarrow \sin\theta = \dfrac{3}{4}$ .
So the answer is (a) $\sin^{-1}\left(\frac{3}{4}\right)$ .

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