First slide

Coherent sources and their importance in interference

Question

A parallel beam of monochromatic light of intensity $I_{0}$ is incident on a glass plate, 25% of light is reflected by upper surface and 50% of light is reflected from lower surface. The ratio of minimum and maximum intensity in interference region of reflected light is

Moderate

A

$\frac{{(\frac{1}{2} - \sqrt{\frac{3}{8}})}^{2}}{{(\frac{1}{2} + \sqrt{\frac{3}{8}})}^{2}}$
B

$\frac{{(1 - \sqrt{2})}^{2}}{{(1 + \sqrt{2})}^{2}}$
C

$\frac{3}{8}$
D

$\frac{4}{9}$

Solution

$I n t e n s i t y o f r e f l e c t e d l i g h t f r o m u p p e r s u r f a c e i s I_{1} = I_{0} \times \frac{25}{100} = \frac{I_{0}}{4} A n d i n t e n s i t y o f t r a n s m i t t e d l i g h t f r o m u p p e r s u r f a c e i s I' = I_{0} - \frac{I_{0}}{4} = \frac{3 I_{0}}{4} T h e i n t e n s i t y o f r e f l e c t e d l i g h t f r o m l o w e r s u r f a c e i s I_{2} = \frac{3 I_{0}}{4} \times \frac{50}{100} = \frac{3 I_{0}}{8} ∴ \frac{I_{\min}}{I_{\max}} = \frac{{(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2}}{{(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}} = \frac{{(\sqrt{\frac{I_{0}}{4}} - \sqrt{\frac{3 I_{0}}{8}})}^{2}}{{(\sqrt{\frac{I_{0}}{4}} + \sqrt{\frac{3 I_{0}}{8}})}^{2}} = \frac{{(\frac{1}{2} - \sqrt{\frac{3}{8}})}^{2}}{{(\frac{1}{2} + \sqrt{\frac{3}{8}})}^{2}}$

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