MHT CET · Physics · Wave Optics
In biprism experiment, if \(5^{\text {th }}\) bright band with wavelength \({ }^{\prime} \lambda_{1}{ }^{\prime}\) coincides with \(6^{\text {th }}\) dark band with wavelength \(^{\prime} \lambda_{2}\) ' then the ratio \(\left(\frac{\lambda_{2}}{\lambda_{1}}\right)\) is
- A \(\frac{10}{11}\)
- B \(\frac{7}{9}\)
- C \(\frac{11}{10}\)
- D \(\frac{9}{7}\)
Answer & Solution
Correct Answer
(A) \(\frac{10}{11}\)
Step-by-step Solution
Detailed explanation
\(y_{5}=\frac{5 \lambda_{1} D}{d}\)
\(y_{6}^{\prime}=\frac{11 \lambda_{2} D}{2 d}\)
\(5 \lambda_{1}=\frac{11 \lambda_{2}}{2}\)
\(\frac{\lambda_{1}}{\lambda_{2}}=\frac{11}{10}\)
\(\therefore \frac{\lambda_{2}}{\lambda_{1}}=\frac{10}{11}\)
\(y_{6}^{\prime}=\frac{11 \lambda_{2} D}{2 d}\)
\(5 \lambda_{1}=\frac{11 \lambda_{2}}{2}\)
\(\frac{\lambda_{1}}{\lambda_{2}}=\frac{11}{10}\)
\(\therefore \frac{\lambda_{2}}{\lambda_{1}}=\frac{10}{11}\)
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