(a) The ratio of the widths of two slits in Young's double-slit experiment is 4 : 1. Evaluate the ratio of intensities at maxima and minima in the interference pattern.
(b) Does the appearance of bright and dark fringes in the interference pattern violate, in any way, conservation of energy ? Explain.

Explanation

To solve the problem, we will break it down into two parts as given in the question.

### Part (a): Evaluate the ratio of intensities at maxima and minima in the interference pattern.

1. **Understanding the problem**:
We have two slits with widths in the ratio of 4:1. Let's denote the width of the first slit as \( a_1 = 4a \) and the width of the second slit as \( a_2 = a \).

2. **Calculating the amplitude of the waves**:
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