Physics Question on wave interference

Question

The fringe width for red colour as compare to that for violet colour is approximately

Answer 1

Solution

The fringe width in a double-slit interference pattern is given by the formula:
w = λL / d
In the case of red and violet light, the wavelength of red light (around 700 nm) is larger than the wavelength of violet light (around 400 nm). Since the fringe width is directly proportional to the wavelength, we can compare the fringe widths by comparing their wavelengths.
Let's denote the fringe width for red light as wr and the fringe width for violet light as wv. If we assume that L and d are the same for both colors, we can compare their fringe widths using the ratio:
wr / wv = λr / λv
Substituting the approximate values for the wavelengths:
wr / wv ≈ 700 nm / 400 nm ≈ 1.75
Therefore, the fringe width for red light is approximately 1.75 times the fringe width for violet light. None of the options (A), (B), (C), or (D) provided match this ratio exactly. However, the closest option is (D) "double," which suggests that the fringe width for red light is double the fringe width for violet light.