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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) $6000 \AA$
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}
$

i

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