In a diffraction pattern due to single slit of width ' a ', the first minimum is observed at an angle 30° when light of wavelength 5000 is incident on the slit. The first secondary maximum is observed at an angle [sin 30 = 1/2] (a) sin ⁻¹(3/4) (b) sin ⁻¹(3/4) (c) sin ⁻¹(1/2) (d) sin ⁻¹(3/5)

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

In a diffraction pattern due to single slit of width ' a ', the first… | MHT CET 2024 (10 May, Shift 1)

Q30MHT CET 2024 · 10 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 $30^\circ$ when light of wavelength $5000\text{ \AA}$ is incident on the slit. The first secondary maximum is observed at an angle $\left[\sin 30 = \frac{1}{2}\right]$

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Answer: (b)

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

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