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  4. A single slit of width a 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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Q. A single slit of width a 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 .

KCETKCET 2005Wave Optics

Solution:

In simple slit diffraction experiment, width of central maxima $y=\frac{2 \lambda D}{d}$
$ \therefore \, \frac{y_{1}}{y_{2}} =\frac{\lambda_{1}}{\lambda_{2}} \times \frac{d_{2}}{d_{1}} $
$=\frac{400}{600} \times \frac{d / 2}{d}=\frac{1}{3}$
$y_{2} =3y $