Interference of Light Waves:

When two coherent light waves superpose, they create an interference pattern. The interference pattern is characterized by bright and dark fringes, which occur due to the constructive and destructive interference of the waves.

Fringe Width:

The fringe width, represented by Δx, is the distance between two consecutive bright or dark fringes on the screen. It is related to the wavelength of light, λ, and the angle α between the two interfering waves.

Explanation:

In this question, we have two coherent plane light waves of equal amplitude making a small angle α. We need to find the fringe width Δx of the interference pattern on the screen.

Using the formula for fringe width:
Δx = λD/d

Where:
λ is the wavelength of light waves
D is the distance between the source and the screen
d is the distance between the two slits or sources of the waves

Now, let's consider a scenario where the two waves are coming from two different slits separated by a distance d. The waves will interfere and create a pattern on the screen.

When the angle α is small, we can approximate sin(α) ≈ α (in radians). This approximation is valid for small angles.

Using this approximation, we can rewrite the formula for fringe width as:
Δx = λD/(αd)

Comparing this equation with the given options, we can see that the correct answer is option 'C':
Δx = λ/(2α)

Explanation of the Correct Answer:

The correct answer is option 'C' because it matches the formula for fringe width given by Δx = λ/(2α).

The fringe width is inversely proportional to the angle α. As the angle α becomes smaller, the fringe width increases. This is because when the angle α is small, the waves interfere over a larger region on the screen, resulting in a wider interference pattern.

Therefore, the correct answer is option 'C': Δx = λ/(2α), which indicates that the fringe width is equal to the wavelength of light divided by twice the angle α.

Δx = λ/(2α)