A single slit of width $d$ is illuminated by violet light of wavelength 400 nm and the width of the diffraction pattern is measured as ' $Y$ '. When half of the slit width is covered and illuminated by yellow light of wavelength 600 nm , the width of the diffraction pattern is

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Aicharya · Accepted Answer

Width of diffraction pattern, $\mathrm{W}=\frac{2 \lambda \mathrm{D}}{\mathrm{~d}}$
When half the slit is covered, $\mathrm{d}^{\prime}=\frac{\mathrm{d}}{2}$ and $\lambda^{\prime}=600 \mathrm{~nm}$ $\begin{array}{ll} \therefore & \mathrm{W}^{\prime}=\frac{2 \lambda^{\prime}}{\mathrm{d} / 2} \\ \therefore & \frac{\mathrm{~W}^{\prime}}{\mathrm{W}}=\frac{2 \lambda^{\prime}}{\lambda}=\frac{2 \times 600}{400} \\ \therefore & \frac{\mathrm{~W}^{\prime}}{\mathrm{W}}=3 \\ \therefore & \mathrm{~W}^{\prime}=3 \mathrm{~W}=3 \mathrm{Y} \end{array}$ ...(given, $\mathrm{W}=\mathrm{Y}$ ) .

A single slit of width $d$ is illuminated by violet light of wavelength 400 nm and the width of the…

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