In a Fraunhoffer diffraction, light of wavelength ' λ ' is incident on slit of width ' d '. The diffraction pattern is observed on a screen placed at a distance ' D '. Th

Question

In a Fraunhoffer diffraction, light of wavelength ' λ ' is incident on slit of width ' d '. The diffraction pattern is observed on a screen placed at a distance ' D '. The linear width of central maximum is equal to two times the width of the slit, then 'D' has value

TestHub · Accepted Answer

The linear width of the central maximum in Fraunhofer diffraction is given by $W = \frac{2 λ D}{d}$ .

Given that the linear width of the central maximum is equal to two times the width of the slit:

$W = 2 d$

Equating the two expressions for $W$ :

$\frac{2 λ D}{d} = 2 d$

$λ D = d^{2}$

$D = \frac{d ^{2}}{λ}$

Answer: $\frac{d ^{2}}{λ}$

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