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Home » Angular width of the central maxima in the Fraunhofer diffraction for is When the same slit is illuminated by another monochromatic light, the angular width decreases by . The wavelength of this light is (1) (2) (3) (4)
Angular width of the central maxima in the Fraunhofer diffraction for \lambda=6000 \AA is \theta_{0^{+}} When the same slit is illuminated by another monochromatic light, the angular width decreases by 30 \%. The wavelength of this light is (1) 420 \mathrm{~A} (2) 1800 \mathrm{~A} (3) 4200 \mathrm{~A} (4) 6000 \AA
Physics | Physics
Angular width of the central maxima in the Fraunhofer diffraction for \lambda=6000 \AA is \theta_{0^{+}} When the same slit is illuminated by another monochromatic light, the angular width decreases by 30 \%. The wavelength of this light is (1) 420 \mathrm{~A} (2) 1800 \mathrm{~A} (3) 4200 \mathrm{~A} (4) 6000 \AA

Answer (3)

Sol. As \theta=\frac{2 \lambda}{a}
\begin{array}{l} \theta_{0}=\frac{2 \times 6000}{\mathbf{a}} \\ \frac{\theta^{\prime}}{\theta_{0}}=\frac{\lambda^{\prime}}{6000} \\ \Rightarrow \lambda^{\prime}=0.7 \times 6000 \quad\left(\text { as } \theta^{\prime}=0.7 \theta_{0}\right) \\ \Rightarrow 4200 \mathrm{~A} \end{array}

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