Question

In an interference experiment the ratio of amplitudes of coherent waves is $\frac{a_1}{a_2} = \frac{1}{3}$ . The ratio of maximum and minimum intensities of fringes will be :

• A. 4
• B. 2
• C. 9
• D. 18

Answer 1

Answer: (A)

4

Answer 2

Given $\frac{a_{1}}{a_{2}} = \frac{1}{3}$
Ratio o f intensities. $\frac{I_{1}}{I_{2}} = \left(\frac{a_{1}}{a_{2}}\right)^{2} = \frac{1}{9}$
Now, $\frac{I_{max }}{I_{max } } = \left(\frac{\sqrt{I_{1}}+\sqrt{I_{2}}}{\sqrt{I_{1}} - \sqrt{I_{2}}}\right)^{2} = \left(\frac{1+3}{1-3}\right)^{2} = 4$