Refraction Through a Glass Prism and Dispersion of Light for CBSE Class 10

When sunlight streams through raindrops after a passing summer storm, a brilliant arch of seven spectral colours paints the sky. How does pure, colorless white sunlight split into the vibrant hues of a rainbow? Is white light a single pure entity, or is it a secret tapestry of multiple colours waiting to be unlocked by an optical prism?

In 1665, the legendary physicist Sir Isaac Newton used a triangular glass prism to demonstrate that white sunlight is a composite mixture of seven distinct spectral colours. In CBSE Class 10 Science, Chapter 10 (The Human Eye and the Colourful World) explores the geometry of refraction through a triangular glass prism, the physics of dispersion (VIBGYOR), and the natural wonder of rainbow formation.

What You Will Learn

• Anatomy of a triangular glass prism: Refracting faces and the Angle of the Prism ($A$)
• Tracing light through a prism: Incident ray, Refracted ray, Emergent ray, and the Angle of Deviation ($D$)
• What is Dispersion of Light?
• Isaac Newton's classic prism experiments: Splitting white light into VIBGYOR
• Why do different colours bend at different angles? The wavelength-speed connection
• Newton's Recombination of Spectrum experiment using an inverted prism
• Atmospheric optics: Step-by-step formation of a natural rainbow
• Board exam ray diagrams, labeling standards, and common student errors

1. Refraction Through a Triangular Glass Prism

A triangular glass prism is a transparent optical medium bounded by two triangular bases and three rectangular lateral refracting surfaces inclined to each other at an angle called the Angle of the Prism ($A$).

Unlike a rectangular glass slab (where opposite refracting faces are parallel, causing the emergent ray to emerge parallel to the incident ray), the refracting faces of a prism are inclined at an angle. Consequently, the emergent ray is permanently deviated from its original path!

                                      A (Angle of Prism)
                                     /                         Incident Ray/   \ Emergent Ray
                        -------> PE/     \FS ------->
                                  /                                        /  EF                                     / (Refracted                               /     Ray)                                  B---------------+ C

Key Angles in the Prism Ray Diagram (NCERT Figure 10.4):

1. $PE$: Incident ray.
2. $EF$: Refracted ray inside the glass prism.
3. $FS$: Emergent ray exiting the prism into air.
4. $\angle A$: Angle of the prism (vertex angle between the two lateral refracting faces).
5. $\angle i$: Angle of incidence (between incident ray and first normal).
6. $\angle r$: Angle of refraction (between refracted ray and first normal).
7. $\angle e$: Angle of emergence (between emergent ray and second normal).
8. The Angle of Deviation ($\angle D$):

   The angle of deviation is the angle formed between the forward-extended incident ray and the backward-extended emergent ray. It measures the total amount by which the light ray has been turned from its original course.

2. Dispersion of White Light by a Glass Prism

When a narrow beam of white sunlight passes through a glass prism, an astonishing phenomenon occurs: the single beam of white light spreads out into a glorious, multi-colored band called a spectrum.

Formal Definition

Dispersion of light is the phenomenon of splitting of composite white light into its constituent seven colours when passed through a transparent refracting medium like a glass prism.

The band of colored components of a light beam is called its spectrum.

    White Sunlight Beam ───> [ PRISM ] ───> RED (Bends LEAST, Top)
                                         ───> ORANGE
                                         ───> YELLOW
                                         ───> GREEN
                                         ───> BLUE
                                         ───> INDIGO
                                         ───> VIOLET (Bends MOST, Bottom)

The Seven Spectral Colours (VIBGYOR):

The sequence of colours from the bottom (maximum deviation) to the top (minimum deviation) is remembered by the famous acronym VIBGYOR:

• V — Violet
• I — Indigo
• B — Blue
• G — Green
• Y — Yellow
• O — Orange
• R — Red

3. Why Does Dispersion Occur? (The Physics of Bending)

Why does white light split into separate colours inside glass?

1. Light is a Mixture of Wavelengths: White light consists of electromagnetic waves of different wavelengths, ranging from approximately $400\text{ nm}$ (violet) to $700\text{ nm}$ (red).
2. Speed in Vacuum vs. Glass: In vacuum or air, all colours of light travel at the exact same speed ($3 \times 10^8\text{ m/s}$).
3. Different Speeds in Material Media: When white light enters a dense optical medium like glass:
   • Red light has the longest wavelength and travels the fastest in glass. Therefore, red light deviates (bends) the LEAST!
   • Violet light has the shortest wavelength and travels the slowest in glass. Therefore, violet light deviates (bends) the MOST!
4. Because each colour bends through a distinctly different angle of refraction, the colours separate into a broad spectrum!

4. Newton's Recombination Experiment (Inverted Prism)

After discovering that a prism splits white light, Isaac Newton sought to determine whether the prism itself produced the colours or if the colours were pre-existing components of sunlight:

           Prism 1 (Upright)                      Prism 2 (Inverted)
                 /\                                      \    /
    White Light /  \     Spectrum of 7 Colours            \  /     Recombined
    ---------> /    \  ==========================>         \/  ---------> WHITE LIGHT!
              /______\                                     /  ```

### The Experimental Setup:
1. Newton placed a second, identical glass prism in an **inverted position** with respect to the first prism.
2. The first upright prism dispersed the incoming white light into its seven constituent spectral colours.
3. All the separated colors then struck the inverted second prism.
4. The second prism bent all seven rays in the reverse direction by the exact same amount, recombining them into a **single, pure emergent beam of white light**!

> **Newton's Landmark Conclusion:** <u>This brilliant experiment proved beyond doubt that the prism does NOT produce colours; white sunlight is naturally composed of a mixture of seven constituent spectral colours!</u>

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## 5. Atmospheric Optics: Formation of a Natural Rainbow

A **rainbow** is a spectacular natural spectrum appearing in the sky after a rain shower.

                        Formation of a Rainbow in a Raindrop
                           Sunlight Beam (From behind observer)
                                                                       \ (1. Refraction & Dispersion)
                      +------------+------------+
                     /     V     R                                      |       \   /                |
                    |        \ /                 |
                    |         x (2. Internal     |
                    |        / \    Reflection)  |
                     \      /   \               /
                      +----+-----+-------------+
                          /       \ (3. Refraction into Air)
                         v         v
                      Violet      Red  ───> Observer's Eye

### Three Conditions for Rainbow Formation:
1. It is always observed in a direction **opposite to that of the Sun** (the Sun must be behind the observer).
2. Tiny, suspended water droplets act like miniature **glass prisms**.
3. **The 3-Step Sequence Inside Each Raindrop (CBSE Core Focus):**
   - **Step 1 (Refraction & Dispersion):** Incident sunlight enters the spherical raindrop, refracts, and disperses into its component colours.
   - **Step 2 (Internal Reflection):** The dispersed rays strike the back curved surface of the droplet and undergo **internal reflection**.
   - **Step 3 (Refraction exiting Drop):** As the rays exit the front face of the water drop back into the air, they undergo a second refraction, bending toward the observer's eyes as a rainbow arc.

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## 6. Summary and Examination Tips

| Colour | Relative Wavelength | Speed in Glass | Extent of Bending (Deviation) |
| :--- | :--- | :--- | :--- |
| **Red** | **Longest** ($pprox 700\text{ nm}$) | **Fastest** | **Deviates the LEAST** (Top of spectrum) |
| **Violet** | **Shortest** ($pprox 400\text{ nm}$) | **Slowest** | **Deviates the MOST** (Bottom of spectrum) |

> **Exam Tip:** In questions asking for the three optical phenomena responsible for a rainbow, write: **(1) Refraction, (2) Dispersion, and (3) Internal reflection**!

> **Common Mistake:** Writing "total internal reflection" for rainbow formation in Class 10. NCERT specifically terms this phenomenon **"internal reflection"** because reflection occurs over a broad range of angles inside the raindrop. Stick strictly to NCERT terminology!