Light of wavelength ' $\lambda$ ' is incident on a slit of width 'd'. The resulting diffraction pattern is…

Light of wavelength ' $\lambda$ ' is incident on a slit of width 'd'. The resulting diffraction pattern is observed on a screen at a distance 'D'. The linear width of the principal maximum is then equal to the width of the slit if $D$ equals
  1. $\frac{\mathrm{d}}{\lambda}$
  2. $\frac{\mathrm{d}^2}{2 \lambda}$
  3. $\frac{2 \lambda}{\mathrm{d}}$
  4. $\frac{2 \lambda^2}{\mathrm{~d}}$

Solution

In diffraction of light by single slit, the width of central maximum is given as $\mathrm{W}_{\mathrm{c}}=\frac{2 \lambda \mathrm{D}}{\mathrm{d}}$ Given: $\mathrm{W}_{\mathrm{c}}=\mathrm{d}$ $\begin{aligned} \therefore \quad d & =\frac{2 \lambda D}{d} \\ & \Rightarrow D=\frac{d^2}{2 \lambda} \end{aligned}$

Asked in: MHT CET 2023 (09 May Shift 2)

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