Problem 46 - Arihant AIEEE Physics

Question

In a glass prism, spectrum is produced due to: (a) refraction (b) dispersion (c) scattering (d) diffraction

Step-by-Step Solution

Answer

Spectrum is produced due to dispersion.

Step 1: Understand Spectrum Formation

A spectrum is formed when light is spread out according to its different wavelengths. This typically happens when light passes through a medium that separates the different colors.

Step 2: Define Key Term - Dispersion

Dispersion is the process by which white light is separated into its constituent colors (spectrum) when it passes through a medium like a prism. This occurs because different wavelengths of light are refracted at slightly different angles, causing them to spread out and form a spectrum.

Step 3: Consider Other Options

While refraction and diffraction also involve bending of light, refraction alone does not separate light into a spectrum, and diffraction involves the bending of light around an object causing interference patterns. Scattering involves the redirection of light in multiple directions, not the separation into a spectrum.

Step 4: Identify the Correct Option

Since the formation of a spectrum in a glass prism is because light is separated into different colors, the correct term that describes this process is 'dispersion.'

Key Concepts

Spectrum Formation

When we mention spectrum formation, we're talking about a fascinating phenomenon where white light splits into its constituent colors. Imagine sunlight hitting raindrops, creating a colorful rainbow. This happens because of spectrum formation. In this process, light is divided into colors based on its varied wavelengths. Each color corresponds to a specific wavelength. For instance, red has longer wavelengths, while violet has shorter ones.
This separation doesn't occur randomly. It takes place when light passes through a medium like a prism, which can differentiate between these wavelengths. The result is a beautiful display of colors, arranged like a rainbow: red, orange, yellow, green, blue, indigo, and violet.

• Spectrum formation occurs when light is divided according to its wavelengths.
• A medium like a prism help achieve this by separating the colors.
• This explains natural spectacles like rainbows.

Understanding spectrum formation enriches our knowledge about how light behaves and interacts with different media.

Wavelength Separation

Wavelength separation is a crucial part of understanding how a spectrum is formed. Each color of light has its own specific wavelength. When light enters a new medium, like glass, these wavelengths change direction at different angles due to a property called refraction. This bending varies because each wavelength travels at different speeds.
The speed variation in glass causes shorter wavelengths (like violet and blue) to bend more than longer wavelengths (like red and orange). The result? Each color scatters differently, creating a visible spread of colors.

• Wavelength separation depends on the speed changes in different mediums.
• The bending difference in wavelengths leads to color separation.
• A slower wavelength in glass results in a greater bending angle.

This principle not only applies to prisms but also explains natural phenomena such as the colorful arcs of rainbows.

Glass Prism Refraction

The role of glass prisms in refraction is central to creating a spectrum. Refraction is the change in light's direction as it passes from one medium to another, like air to glass. This happens because light travels at different speeds in different materials.
In a glass prism, when white light enters, it's refracted or bent at two surfaces - the entry and the exit. This bending is what leads to the dispersion of light into its constituent colors. Each of these colors bends at a slightly different angle due to their different wavelengths.

• Refraction in a prism involves bending light at two surfaces.
• Different wavelengths refract differently because of speed variations.
• This refraction and subsequent dispersion give us a complete color spectrum.

Hence, a simple glass prism is a powerful tool for demonstrating how light can be split into its vibrant colors using the principle of refraction.