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  4. A ray of light of intensity I is incident on a parallel glass-slab at a point A as shown in fig. It undergoes partial reflection and refraction. At each reflection 25 % of incident energy is reflected. The rays A B and A' B' undergo interference. The ratio I max / I min is

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Q. A ray of light of intensity $I$ is incident on a parallel glass-slab at a point $A$ as shown in fig. It undergoes partial reflection and refraction. At each reflection $25 \%$ of incident energy is reflected. The rays $A B$ and $A' B'$ undergo interference. The ratio $I_{\max } / I_{\min }$ isPhysics Question Image

Wave Optics

Solution:

From figure $I_{1}=\frac{I}{4}$ and $I_{2}=\frac{9 I}{64} \Rightarrow \frac{I_{2}}{I_{1}}=\frac{9}{16}$
image
By using $\frac{I_{\max }}{I_{\min }}=\left(\frac{\sqrt{\frac{I_{2}}{I_{1}}}+1}{\sqrt{\frac{I_{2}}{I_{1}}}-1}\right)$
$=\left(\frac{\sqrt{\frac{9}{16}}+1}{\sqrt{\frac{9}{16}}-1}\right)=\frac{49}{1}$