Light: Refraction Through Prism and Dispersion of Light Class 10

When a narrow beam of pure white sunlight strikes the tilted face of a triangular glass prism, it emerges not as white light, but as a dazzling fan of seven brilliant colors: Red, Orange, Yellow, Green, Blue, Indigo, and Violet. For centuries, philosophers believed that the glass magically dyed or stained the white light. It took the genius of Sir Isaac Newton in 1666 to prove the opposite: white light is not pure, but an intricate mixture of all the colors of the rainbow!

In CBSE Class 10 Science, Chapter 10 (The Human Eye and the Colourful World), the Refraction of Light Through a Triangular Glass Prism, the physics of Dispersion, Newton's Recombination Experiment, and the natural optics of Rainbow Formation carry between $4$ and $6$ marks.

In this master guide, we break down the geometric ray paths, deviation formulas, and optical principles.

What You Will Learn

• Geometric anatomy of a Triangular Glass Prism: Angle of Prism ($A$) and Angle of Deviation ($D$)
• The fundamental angle relationship: $A + D = i + e$
• What is Dispersion of Light? The wave-speed mechanism ($v_{\text{red}} > v_{\text{violet}}$)
• Sir Isaac Newton's classic Spectrum Recombination Experiment (Inverted prism)
• The 3-Step Atmospheric Physics of Rainbow Formation
• High-yield ray diagrams, examiner tips, and common board traps

1. Refraction Through a Triangular Glass Prism

A triangular glass prism has two triangular bases and three rectangular lateral refracting surfaces inclined at an angle called the Angle of the Prism ($A$):

                                      A (Angle of Prism)
                                     /                         Incident    /                             Ray  ───>+     +───> Emergent Ray
                                  / \   / \     (Deviated by Angle D!)
                                 /   \ /                                   B-----+-----C

The Ray Tracing Sequence:

1. At First Surface ($AB$): Light enters from optically rarer air into denser glass $\implies$ bends TOWARDS the normal.
2. At Second Surface ($AC$): Light exits from denser glass into rarer air $\implies$ bends AWAY from the normal.
3. The Emergent Ray: Notice that unlike a rectangular glass slab (where refracting faces are parallel), the faces of a prism are inclined.
   • Therefore, <u>the emergent ray is NOT parallel to the incident ray; it is bent significantly towards the thicker base of the prism!</u>

The Angle of Deviation ($D$):

The angle between the extended path of the incident ray and the emergent ray is called the Angle of Deviation ($D$): $\mathbf{A + D = i + e}$

• $A$: Angle of Prism
• $D$: Angle of Deviation
• $i$: Angle of Incidence
• $e$: Angle of Emergence

2. What is Dispersion of Light?

Definition

Dispersion of light is the phenomenon of splitting of a beam of white light into its seven constituent spectral colors upon passing through a transparent refracting medium like a glass prism.

The band of colored components is called a Spectrum, memorized by the acronym VIBGYOR: $\mathbf{V\text{iolet} \longrightarrow I\text{ndigo} \longrightarrow B\text{lue} \longrightarrow G\text{reen} \longrightarrow Y\text{ellow} \longrightarrow O\text{range} \longrightarrow R\text{ed}}$

                       White Light Beam ───> [ PRISM ] ───> Red (Bends LEAST!)
                                                             Orange
                                                             Yellow
                                                             Green
                                                             Blue
                                                             Indigo
                                                             Violet (Bends MOST!)

Why Do Different Colors Bend at Different Angles? (The Physical Cause)

1. In a vacuum, all colors of light travel at the exact same speed ($3 \times 10^8\text{ m/s}$).
2. However, inside glass, different colors travel at different speeds:
   • Red light has the longest wavelength ($\approx 700\text{ nm}$) and travels fastest in glass $\implies$ has the smallest refractive index ($n_{\text{red}}$) $\implies$ bends the LEAST!
   • Violet light has the shortest wavelength ($\approx 400\text{ nm}$) and travels slowest in glass $\implies$ has the highest refractive index ($n_{\text{violet}}$) $\implies$ bends the MOST!
3. <u>Because each color refracts through a different angle of deviation, white light fans out into a distinct spectrum!</u>

3. Newton's Spectrum Recombination Experiment

How did Newton prove that the prism does not create colors, but merely separates colors already present in white light?

               Prism P₁ (Upright)                     Prism P₂ (INVERTED!)
                      A                                     B'-----C'
                     / \                                     \     /
       White Light  /   \  Spectrum (VIBGYOR)                 \   /  White Light Emerges!
          ───────> +     + ─────────────────────────────────>  + +  ───────────────────>
                  /       \                                     \ /
                 B---------C                                     A'
            Splits into Spectrum                   Recombines into WHITE LIGHT!

The Experimental Setup:

1. Newton placed a second, identical glass prism $P_2$ in an inverted position relative to the first upright prism $P_1$.
2. The first prism $P_1$ dispersed the white light into its seven constituent colors.
3. The inverted second prism $P_2$ received all seven colors and bent them in the exact opposite direction by equal amounts!
4. The Observation: A beam of pure white light emerged from the other side of the second prism!
5. <u>This celebrated experiment proved conclusively that white sunlight is composed of seven constituent spectral colors!</u>

4. The Atmospheric Physics of Rainbow Formation

A rainbow is a natural spectrum appearing in the sky after a rain shower:

                            Sunlight Ray enters Raindrop
                                                                                 \  (1. REFRACTION + DISPERSION)
                                    (  •  )
                                   /       \  (2. INTERNAL REFLECTION at back wall)
                                  v         v
                                   \       /
                                    \_____/
                                                                               v  (3. REFRACTION out into observer's eye!)

The Three Sequential Optical Steps:

Tiny spherical raindrops suspended in the atmosphere act like miniature glass prisms:

1. Refraction and Dispersion: As parallel sunlight enters a spherical raindrop, it refracts and splits into its seven component colors.
2. Internal Reflection: The dispersed rays strike the curved back wall of the water droplet and undergo internal reflection.
3. Refraction out of Droplet: As light exits the front surface of the raindrop back into air, it refracts again, fanning out into an arc of colors.

Condition for Observing a Rainbow: <u>A rainbow is always formed in a direction OPPOSITE to that of the Sun! The observer must stand with their back turned towards the Sun.</u>

5. Summary and Examination Tips

Exam Tip: In questions asking for the three optical processes that produce a rainbow, list them in exact chronological order: (1) Refraction, (2) Dispersion, (3) Internal Reflection, and (4) Refraction!

Common Mistake: Stating that a rainbow is caused by Total Internal Reflection (TIR). CBSE board criteria accept "internal reflection" because the reflection at the back of the raindrop is not necessarily at an angle exceeding the critical angle; calling it strictly "internal reflection" safeguards full marks!