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  4. Angular width of central maxima in the Fraunhofer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength 6000 mathringA. When the slit is illuminated by light of another wavelength, the angular width decreases by 30 %. The wavelength of this light will be

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Q. Angular width of central maxima in the Fraunhofer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength $6000 \,\mathring{A}$. When the slit is illuminated by light of another wavelength, the angular width decreases by $30 \%$. The wavelength of this light will be

Wave Optics

Solution:

Angular width $\beta=\frac{2 \lambda}{d}$
$\Rightarrow \frac{\beta_{1}}{\beta_{2}}=\frac{\lambda_{1}}{\lambda_{2}} $
$\Rightarrow \frac{\beta}{\frac{70}{100} \beta}=\frac{6000}{\lambda_{2}} $
$\Rightarrow \lambda_{2}=4200 \,\mathring{A}$