Chapter 27, Problem 1FC

To determine

The difference $l_2-l_1$ in the two path lengths.

Answer to Problem 1FC

The correct option is (e) $\underset{\_}{\frac{5}{2}\lambda }$.

Explanation of Solution

There will be a difference between the path length $l_2$ and $l_1$ occurs only when the distance between the path lengths differ by an odd integer number of half wavelengths. This corresponds to $\frac{\lambda }{2}$ , $\frac{3\lambda }{2}$ , $\frac{5\lambda }{2}$ and so on. When the path difference is $\frac{\lambda }{2}$, the first intensity minimum will occur.

Hence the third will occur when path difference is $\frac{5\lambda }{2}$.

Conclusion:

Hence, the correct option is (e) $\underset{\_}{\frac{5}{2}\lambda }$.