(a) Define prism angle and angle of deviation for a prism.

(b) Write the sequence of colors in the spectrum formed by the passage of white light through a prism.

(c) Explain the process of formation of a rainbow.

Let’s break down your questions about prisms and rainbows step by step. Understanding these concepts not only helps in grasping the principles of optics but also enhances our appreciation of natural phenomena like rainbows.

Understanding Prism Angle and Angle of Deviation

A prism is a transparent optical element with flat, polished surfaces that refract light. The prism angle, also known as the apex angle, is the angle formed between the two plane surfaces of the prism. It is crucial because it determines how much the light will bend as it passes through the prism.

The angle of deviation refers to the angle by which the light ray is deviated from its original path after passing through the prism. This angle is influenced by the prism angle and the refractive index of the material. When light enters a prism, it slows down and bends due to the change in medium, and the angle of deviation quantifies this bending.

Color Spectrum from White Light

When white light passes through a prism, it disperses into its constituent colors due to different wavelengths bending by varying amounts. The sequence of colors observed in the spectrum is:

• Red
• Orange
• Yellow
• Green
• Blue
• Indigo
• Violet

This sequence is often remembered by the acronym ROYGBIV. Each color corresponds to a different wavelength, with red having the longest wavelength and violet the shortest. The varying degrees of bending lead to this beautiful spectrum.

Formation of a Rainbow

The process of rainbow formation is a fascinating interplay of light and water droplets in the atmosphere. Here’s how it works:

1. **Refraction**: When sunlight enters a raindrop, it slows down and bends due to the change in medium from air to water. This bending is similar to what happens in a prism.

2. **Dispersion**: As the light refracts, it separates into its constituent colors because different wavelengths of light bend at different angles. This is the same principle that creates the color spectrum in a prism.

3. **Reflection**: Inside the raindrop, the light reflects off the inner surface of the droplet. This internal reflection causes the light to travel back towards the front of the droplet.

4. **Refraction Again**: As the light exits the droplet, it refracts once more, further separating the colors. The angle at which the light exits determines the observer's perspective of the rainbow.

5. **Viewing Angle**: A rainbow is typically seen when the sun is behind the observer and rain is falling in front. The colors appear in a circular arc, with red on the outer edge and violet on the inner edge.

In summary, the prism angle and angle of deviation are fundamental concepts in optics that explain how light behaves when passing through a prism. The sequence of colors formed by white light is a direct result of this behavior, and the formation of a rainbow is a beautiful natural phenomenon that showcases the same principles of refraction and dispersion. Understanding these concepts not only deepens our knowledge of light but also enhances our appreciation for the wonders of nature.