MHT CET · Physics · Wave Optics
In Young's double slit experiment, the ' \(\mathrm{n}^{\text {th ' }}\) maximum of wavelength ' \(\lambda_1\) ' is at a distance ' \(y_1\) ' from the central maximum. When the wavelength of the source is changed to ' \(\lambda_2\) ', \(\left(\frac{\mathrm{n}}{2}\right)^{\text {th }}\) maximum is at ' \(\mathrm{y}_2\) ' from its central maximum. The ratio \(\frac{\mathrm{y}_1}{\mathrm{y}_2}\) is
- A \(\frac{\lambda_1}{\lambda_2}\)
- B \(\frac{2 \lambda_1}{\lambda_2}\)
- C \(\frac{2 \lambda_2}{\lambda_1}\)
- D \(\frac{\lambda_1}{2 \lambda_2}\)
Answer & Solution
Correct Answer
(B) \(\frac{2 \lambda_1}{\lambda_2}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{y}_1=\mathrm{n} \beta_1=\frac{\mathrm{n} \lambda_1 \mathrm{D}}{\mathrm{d}}\) and \(\mathrm{y}_2=\frac{\mathrm{n}}{2} \beta_2=\frac{\mathrm{n} \lambda_2 \mathrm{D}}{2 \mathrm{~d}}\)
\(
\therefore \frac{\mathrm{y}_1}{\mathrm{y}_2}=\frac{2 \lambda_1}{\lambda_2}
\)
\(
\therefore \frac{\mathrm{y}_1}{\mathrm{y}_2}=\frac{2 \lambda_1}{\lambda_2}
\)
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