Question

Two coherent sources of intensity ratio b interfere. Find the ratio in the interference pattern –

• A. $\frac{2\sqrt{\beta}}{1 + \beta}$
• B. $\frac{2\beta}{1 + \beta}$
• C. $\frac{\sqrt{\beta} + 1}{\sqrt{\beta} - 1}$
• D. $\frac{\sqrt{\beta}}{1 + \sqrt{\beta}}$

Answer 1

Answer: (A)

$\frac{2\sqrt{\beta}}{1 + \beta}$

Answer 2

It is given $\frac{a_{1}}{a_{2}}$=$\sqrt{\frac{I_{1}}{I_{2}}}$=$\sqrt{\beta}$

I_max = (a₁ + a₂)²

I_min = (a₁ – a₂)²

=$\frac{(a_{1} + a_{2})^{2} - (a_{1} - a_{2})^{2}}{(a_{1} + a_{2})^{2} + (a_{1} - a_{2})^{2}}$=$\frac{2a_{1}a_{2}}{a_{1}^{2} + a_{2}^{2}}$=$\frac{2\left( \frac{a_{1}}{a_{1}} \right)}{\left( \frac{a_{1}}{a_{1}} \right)^{2} + 1}$

=$\frac{2\sqrt{\beta}}{\beta + 1}$