A single slit of width b is illuminated by a coherent monochromatic… | JEE Main 2017 (8 Apr, Shift 1)

Q75JEE Main 2017 · 8 APR · SHIFT 1Medium

Diffraction at a Single Slit

A single slit of width b is illuminated by a coherent monochromatic light of wavelength $\lambda$ . If the second and fourthminima 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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Answer: (b)

Minima on the screen: $y_n = \dfrac{nD\lambda}{b}$ .
$y_2 = 3\text{ cm} \Rightarrow \dfrac{D\lambda}{b} = 1.5\text{ cm}$ (consistent with $y_4 = 6\text{ cm}$ ).
Width of central maximum $= 2\dfrac{D\lambda}{b} = 3.0\text{ cm}$ .
So the answer is (b) $3.0\text{ cm}$ .

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