JEE Main · 2005 · 08 May 2005 · Offline · Wave Optics

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I_{0}

is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

(A) $2 I_{0}$
(B) $4 I_{0}$ ✓ Correct
(C) $I_{0}$
(D) $I_{0} /2$

Answer: (B)

Solution

At the centre of a single-slit pattern every Huygens wavelet from across the opening arrives in step, so the resultant amplitude grows in proportion to the slit width and the peak intensity grows as the square of the width. Doubling the width therefore makes the central intensity four times as large,

4 I_{0}

. An energy check agrees: a wider slit passes twice the power yet squeezes the central fringe to half its angular width, so the peak must climb fourfold. Calling the maximum 'independent of slit width' mistakes the normalised shape of the pattern for its actual height.

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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JEE Main · 2005 · 08 May 2005 · Offline · Wave Optics

Solution

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