Question

Two coherent sources of light interfere. The intensity ratio of two sources is 1 : 4. For this interference pattern if the value of
$\frac{I_{max}+I_{min}}{I_{max}-I_{min}}$is equal to $\frac{2α+1}{β+3},$
then α/β will be

• A. 1.5
• B. 2
• C. 0.5
• D. 1

Answer 1

Answer: (B)

2

Answer 2

The correct answer is (B) : 2
$I_{max} = (\sqrt{I_1}+\sqrt{I_2})^2$
$I_{min} = (\sqrt{I_1}-\sqrt{I_2})^2$
$∴ \frac{I_{max}+I_{min}}{I_{max}-I_{min}} = \frac{2(I_1+I_2)}{4×\sqrt{I_1I_2}}$
$=\frac{1}{2} ×\frac{(\frac{I_1}{I_2}+1)}{\sqrt{\frac{I_1}{I_2}}}$
$= \frac{1}{2} ×\frac{(\frac{1}{4}+1)}{(\frac{1}{2})}$
$= \frac{5}{4} = \frac{2×2+1}{1+3}$
$∴ \frac{α}{β} = \frac{2}{1} = 2$