in a single-slit diffraction pattern , the width of the slit is made double its original width then the centre maximum of diffraction pattern will become

When you increase the width of a single slit in a diffraction experiment, it has a direct impact on the diffraction pattern observed on a screen. Specifically, if you double the width of the slit, the central maximum of the diffraction pattern will become narrower. Let’s break down why this happens.

The Basics of Single-Slit Diffraction

In a single-slit diffraction setup, light passes through a narrow slit and spreads out, creating a pattern of bright and dark fringes on a screen. The central maximum is the brightest and widest part of this pattern, and it occurs directly in line with the slit.

Understanding the Relationship Between Slit Width and Diffraction

The diffraction pattern can be described using the formula for the angular position of the minima, which is given by:

• a sin(θ) = mλ

Here, a is the width of the slit, θ is the angle at which the minima occur, m is the order of the minimum (1, 2, 3, ...), and λ is the wavelength of the light used.

Effect of Doubling the Slit Width

When you double the width of the slit from a to 2a, the equation for the minima becomes:

• 2a sin(θ) = mλ

This means that for the same order of minimum m, the angle θ will decrease. In simpler terms, the positions of the dark fringes will move closer to the center, resulting in a narrower central maximum.

Visualizing the Change

Imagine the original diffraction pattern as a wide, spread-out wave. When you narrow the slit, the wavefronts are more concentrated, leading to a sharper peak. This is akin to how a water wave becomes more focused when it passes through a narrower opening, creating a more pronounced wave crest.

Summary of Changes

To summarize, when the width of the slit is doubled:

• The central maximum becomes narrower.
• The overall intensity of the central maximum may increase, but its width decreases.

This principle is crucial in understanding wave behavior and has applications in various fields, including optics and engineering. By manipulating the slit width, you can control the diffraction pattern, which is essential in designing optical instruments and understanding wave phenomena.