MHT CET · Physics · Wave Optics
The angular separation of the central maximum in the Fraunhofer diffraction pattern is measured. The slit is illuminated by the light of wavelength \(6000 Å\). If the slit is illuminated by light of another wavelength, the angular separation decreases by \(20 \%\). The wavelength of light used is
- A \(6400 Å\)
- B \(5600 Å\)
- C \(4800 Å\)
- D \(4400 Å\)
Answer & Solution
Correct Answer
(C) \(4800 Å\)
Step-by-step Solution
Detailed explanation
The angular width of central maximum is
\(\begin{array}{ll}
& \theta=\frac{2 \lambda}{\mathrm{a}} \Rightarrow \theta \propto \lambda \\
& \frac{\theta_2}{\theta_1}=\frac{\lambda_2}{\lambda_1} \\
& \text { For } \theta_2=\theta_1-\frac{20}{100} \theta_1=0.8 \theta_1 \\
\therefore \quad & \lambda_2=0.8 \lambda_1=0.8 \times 6000=4800 Å
\end{array}\)
\(\begin{array}{ll}
& \theta=\frac{2 \lambda}{\mathrm{a}} \Rightarrow \theta \propto \lambda \\
& \frac{\theta_2}{\theta_1}=\frac{\lambda_2}{\lambda_1} \\
& \text { For } \theta_2=\theta_1-\frac{20}{100} \theta_1=0.8 \theta_1 \\
\therefore \quad & \lambda_2=0.8 \lambda_1=0.8 \times 6000=4800 Å
\end{array}\)
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