Problem 5 - Master Resource Book in JEE Main Physics

Question

Consider sunlight incident on a slit of width \(10^{4} \mathrm{~A}\). The image seen through the slit shall [NCERT Exemplar] (a) be a fine sharp slit white in colour at the centre (b) a bright slit. white at the centre diffusing to zero intensities at the edges (c) a bright slit white at the centre diffusing to regions of different colours (d) Only be a diffused slit white in colour

Step-by-Step Solution

Answer

The image will be a bright slit white at the center diffusing to regions of different colors (option c).

Step 1: Understanding Diffraction

When light passes through a narrow slit, it undergoes diffraction, spreading out and forming a pattern rather than a single line.

Step 2: Concept of Wavelength and Slit Width

The given slit width is \(10^4 \) Å (Angstroms), which is approximately the same order of size as the wavelength of visible light (4000 Å to 7000 Å), causing noticeable diffraction effects.

Step 3: Diffraction Pattern Expectation

Diffraction through a narrow slit leads to the formation of a central bright maximum with progressively weaker and more colorful maxima and minima on either side due to varying interference of light waves at different angles.

Step 4: Analyze the Options

The description of a central bright region that diffuses into different colors matches the diffraction pattern resulting from different wavelengths of light being split at different angles. Hence, the correct observation would be a bright slit in the center spreading out to different colors.

Key Concepts

Wavelength

The term 'wavelength' refers to the distance between consecutive peaks of a wave. In the context of light, wavelength determines the color we perceive. Light with shorter wavelengths appears blue or violet, whereas longer wavelengths appear red. The range of wavelengths for visible light is approximately 4000 Å to 7000 Å. Understanding wavelength is crucial in the study of diffraction because it directly affects how light interacts with objects, such as a slit or an obstacle.

When light with a certain wavelength encounters a slit, the size of the slit relative to the wavelength can determine the extent of diffraction. If the slit size is comparable to the wavelength, as in the given example where the slit width is 10000 Å, light undergoes significant diffraction. This interaction creates distinctive patterns that are vital for analyzing light behavior in optical physics.

Diffraction Pattern

A diffraction pattern is an arrangement of light and dark bands resulting from the bending of light waves around an obstacle or passing through a narrow opening, such as a slit. When sunlight, which is made up of different wavelengths (colors), passes through a slit, these wavelengths bend at slightly different angles, creating an array of colors.

The most noticeable feature of a diffraction pattern is the central maximum—a bright spot located at the center of the pattern. This is usually followed by multiple fringes or bands of gradually decreasing brightness. These bands are colorful due to the separation of light into its component wavelengths, akin to a prism's effect on light. As these light waves overlap and interfere with each other, it leads to regions of constructive and destructive interference, forming the familiar pattern of light and dark bands.

Interference of Light Waves

Interference occurs when two or more light waves overlap and combine. The outcome can either be constructive (amplifying light intensity) or destructive (reducing light intensity). In diffraction, this principle is at work as the waves passing through different parts of the slit interfere with each other.

• Constructive Interference: When the peaks of different waves align, they add together, resulting in a brighter light region, known as fringes or maxima.
• Destructive Interference: When the peak of one wave aligns with the trough of another, they cancel each other out, creating a dark region or minima.

This interference of light waves is crucial to forming the beautiful patterns we see in diffraction. It explains why the central region is bright (where many waves constructively interfere) and why we get regions of varying intensity and color, especially when dealing with a broad spectrum like sunlight.