Question:
A single slit of width b is illuminated by a coherent monochromatic light of wavelength \(\lambda\). If the second and fourth minima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum ? (i.e. distance between first minimum on either side of the central maximum)
A single slit of width b is illuminated by a coherent monochromatic light of wavelength \(\lambda\). If the second and fourth minima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum ? (i.e. distance between first minimum on either side of the central maximum)
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The n-th minimum is at \(y_n = n\lambda D/b\), so the minima are equally spaced from the centre; first minimum lies at \(y_1 = y_2/2\).
Updated On: Nov 11, 2026
- 1.5 cm
- 3.0 cm
- 4.5 cm
- 6.0 cm
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The Correct Option is B
Solution and Explanation
For a single slit, the n-th minimum is at \(y_n = \dfrac{n\lambda D}{b}\).
Second minimum: \(y_2 = \dfrac{2\lambda D}{b} = 3\) cm, so \(\dfrac{\lambda D}{b} = 1.5\) cm.
Check with the fourth minimum: \(y_4 = 4 \times 1.5 = 6\) cm, which matches the given data.
First minimum: \(y_1 = \dfrac{\lambda D}{b} = 1.5\) cm.
Width of central maximum \(= 2y_1 = 2 \times 1.5 = 3.0\) cm.
Answer: (2) 3.0 cm
Second minimum: \(y_2 = \dfrac{2\lambda D}{b} = 3\) cm, so \(\dfrac{\lambda D}{b} = 1.5\) cm.
Check with the fourth minimum: \(y_4 = 4 \times 1.5 = 6\) cm, which matches the given data.
First minimum: \(y_1 = \dfrac{\lambda D}{b} = 1.5\) cm.
Width of central maximum \(= 2y_1 = 2 \times 1.5 = 3.0\) cm.
Answer: (2) 3.0 cm
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