A parallel beam of light of intensity I0 is incident on a coated glass plate. If 25 % of the incident light is reflected from the upper surface and 50 % of light is reflected from the lower surface of the glass plate, the ratio of maximum to minimum intensity in the interference region of the reflected light is

Question

A parallel beam of light of intensity I0 is incident on a coated glass plate. If 25 % of the incident light is reflected from the upper surface and 50 % of light is reflected from the lower surface of the glass plate, the ratio of maximum to minimum intensity in the interference region of the reflected light is (A) (((1/2) + √(3/8)/(1)2- √(3)8)/2)  (B) (((1/4) + √(3/8)/(1)2- √(3)8)/2)  (C) (5/8) (D) (8/5)

Tardigrade Admin · Accepted Answer

According to question, we can draw the following diagram

I_{1} = \frac{I _{0}}{4} \Rightarrow I_{2} = \frac{3}{8} I_{0}

We know that,

\frac{I _{m a x}}{I _{m i n}} = \frac{( I _{1} + I _{2} ) ^{2}}{( I _{1} - I _{2} ) ^{2}} = (\frac{\frac{1}{2} + \frac{3}{8}}{\frac{1}{2} - \frac{3}{8}})^{2}

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

$(\frac{\frac{1}{4} + \frac{3}{8}}{\frac{1}{2} - \frac{3}{8}})^{2}$

$\frac{5}{8}$

$\frac{8}{5}$

According to question, we can draw the following diagram

$I_{1} = \frac{I _{0}}{4} \Rightarrow I_{2} = \frac{3}{8} I_{0}$
We know that,
$\frac{I _{m a x}}{I _{m i n}} = \frac{( I _{1} + I _{2} ) ^{2}}{( I _{1} - I _{2} ) ^{2}} = (\frac{\frac{1}{2} + \frac{3}{8}}{\frac{1}{2} - \frac{3}{8}})^{2}$

(21​−83​​21​+83​​​)2

(21​−83​​41​+83​​​)2

85​

58​

According to question, we can draw the following diagram I1​=4I0​​⇒I2​=83​I0​ We know that, Imin​Imax​​=(I1​​−I2​​)2(I1​​+I2​​)2​=(21​−83​​21​+83​​​)2

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

$(\frac{\frac{1}{4} + \frac{3}{8}}{\frac{1}{2} - \frac{3}{8}})^{2}$

$\frac{5}{8}$

$\frac{8}{5}$

According to question, we can draw the following diagram

$I_{1} = \frac{I _{0}}{4} \Rightarrow I_{2} = \frac{3}{8} I_{0}$
We know that,
$\frac{I _{m a x}}{I _{m i n}} = \frac{( I _{1} + I _{2} ) ^{2}}{( I _{1} - I _{2} ) ^{2}} = (\frac{\frac{1}{2} + \frac{3}{8}}{\frac{1}{2} - \frac{3}{8}})^{2}$