MHT CET · Physics · Wave Optics
In Young's double slit experiment, the ratio of intensities at two points on a screen when waves from the two slits have a path difference of zero and \(\frac{\lambda}{4}\) is
\(\left[\cos 0^{\circ}=\sin 90^{\circ}=1, \sin 0^{\circ}=\cos 90^{\circ}=0\right]\)
- A \(2: 1\)
- B \(3: 1\)
- C \(2: 3\)
- D \(3: 2\)
Answer & Solution
Correct Answer
(A) \(2: 1\)
Step-by-step Solution
Detailed explanation
\(I=4 I_{0} \cos ^{2} \frac{\phi}{2}\)
\(\phi=\frac{2 \pi}{\lambda} \times \frac{\lambda}{4}=\frac{\pi}{2}\)
\(\frac{\phi}{2}=\frac{\pi}{4}\)
\(\frac{1}{I_{0}}=4 \cos ^{2} \frac{\pi}{4}=\frac{4}{2}=2: 1\)
\(\phi=\frac{2 \pi}{\lambda} \times \frac{\lambda}{4}=\frac{\pi}{2}\)
\(\frac{\phi}{2}=\frac{\pi}{4}\)
\(\frac{1}{I_{0}}=4 \cos ^{2} \frac{\pi}{4}=\frac{4}{2}=2: 1\)
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