Animated Solution for Physics - Optics: In Young's double slit experiment, if the source of light changes from orange to blue, then

Imagine you are standing in a dark room, observing a classic Young's Double Slit Experiment. We start by shining a bright orange light through two narrow, closely spaced slits.

As the light waves emerge from the slits, they overlap and interfere with each other. When you look at the screen placed at a distance, you don't just see a blob of light. Instead, you see a beautiful, alternating pattern of bright and dark bands.

These bands are called interference fringes. The distance between the centers of two consecutive bright fringes, or two consecutive dark fringes, is a crucial parameter known as the fringe width.

To understand how this pattern behaves, we need to look at the mathematics governing it. The fringe width, denoted by the Greek letter $\beta$, is given by a very elegant formula:

Let's break down what each of these variables means in the physical world. Here, $D$ represents the macroscopic distance between the plane of the slits and the screen. The small $d$ is the microscopic separation between the two slits themselves.

Finally, $\lambda$ is the wavelength of the incident light. This equation is powerful because it tells us exactly how the fringe width responds to changes in our experimental setup.

Orange to Blue

The problem presents us with a specific scenario: what happens if we change our light source from orange to blue?

To answer this, we must recall the visible light spectrum, often remembered by the acronym VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red). As we move from violet to red, the wavelength of the light increases.

Therefore, it is a fundamental fact that the wavelength of blue light is strictly less than the wavelength of orange light. Mathematically, we can write this as:

Now, let's bring our master equation back into the picture. In our scenario, we are only changing the color of the light. We are not moving the screen, nor are we changing the slits.

This means that both $D$ and $d$ remain perfectly constant. Looking at the formula $\beta =\frac{D\lambda }{d}$, it is crystal clear that the fringe width $\beta$ is directly proportional to the wavelength $\lambda$.

Since the wavelength decreases when we switch from orange to blue light, the fringe width must also decrease proportionally.

Visually, this means the entire interference pattern shrinks. The bright and dark bands squeeze closer together. Consequently, the distance between consecutive fringes will decrease, making option (b) the correct answer.