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

The Correct Option is B

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