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 illumin

Question

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

TestHub · Accepted Answer

The width of the central maximum in a single slit diffraction pattern is given by $Y = \frac{2 λ D}{d}$ , where $λ$ is the wavelength, $D$ is the distance to the screen, and $d$ is the slit width.

For the first case, $λ_{1} = 400$ nm and the slit width is $d$ .

$Y = \frac{2 \times 400 \times D}{d} = \frac{800 D}{d}$

For the second case, half of the slit is covered, so the new slit width is $d^{'} = \frac{d}{2}$ . The new wavelength is $λ_{2} = 600$ nm.

$Y^{'} = \frac{2 \times 600 \times D}{\frac{d}{2}} = \frac{2400 D}{d}$

Taking the ratio of the two widths:

$\frac{Y ^{'}}{Y} = \frac{2400}{800} = 3$

$Y^{'} = 3 Y$

Answer: 3 Y

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