Refraction of Light, Snell's Law, and Refractive Index for CBSE Class 10

Have you ever placed a pencil in a transparent glass of water and noticed that it appears bent or broken at the water-air boundary? Or observed that a coin placed at the bottom of a water cup appears raised above its actual position? Or seen the letters of a book appear elevated when viewed through a thick glass paperweight?

These everyday visual optical illusions are governed by the same fundamental phenomenon of physics: the refraction of light. In CBSE Class 10 Science, Chapter 9 (Light - Reflection and Refraction) uncovers why light changes its direction when passing between transparent media and introduces Snell's Law and the Refractive Index.

What You Will Learn

• What is refraction of light and why does it occur?
• Optically rarer vs. optically denser media: Bending rules
• Refraction through a rectangular glass slab and lateral displacement
• The Two Laws of Refraction and Snell's Law
• Relative refractive index vs. Absolute refractive index ($n = c / v$)
• Optical density vs. Mass density (The Kerosene-Water Paradox)
• Board exam numerical problems and common misconceptions

1. What is Refraction of Light?

Definition

The refraction of light is the phenomenon of the bending of a light ray as it passes obliquely from one transparent optical medium into another having a different optical density.

Why Does Light Bend? (The Cause of Refraction)

Light travels as a wave at a fixed speed of approximately $3 \times 10^8\text{ m/s}$ in vacuum or air. However, when light enters transparent material media (such as water, glass, or alcohol), it interacts with the electron clouds of the atoms, slowing down.

The Root Cause: <u>Refraction occurs because the SPEED OF LIGHT is different in different media!</u>

2. Bending Rules: Optically Rarer vs. Denser Media

Optical density is a measure of how much a medium slows down light:

• Optically Rarer Medium: Light travels faster (e.g., Air).
• Optically Denser Medium: Light travels slower (e.g., Glass, Water).

    Case 1: Rarer to Denser (e.g., Air → Glass)     Case 2: Denser to Rarer (e.g., Glass → Air)
                    Normal                                          Normal
                      |                                               |
         Incident Ray \                                  Incident Ray                        \ ∠i                                            \ ∠i
         ~~~~~~~~~~~~~~~+~~~~~~~~~~~~~~~                 ~~~~~~~~~~~~~~~+~~~~~~~~~~~~~~~
                       / ∠r                                              \ ∠r
                      /                                                             Bends TOWARDS Normal (∠i > ∠r)                  Bends AWAY FROM Normal (∠i < ∠r)

1. Rarer to Denser (Slows Down): When light travels from an optically rarer to an optically denser medium, the ray bends towards the normal ($\angle i > \angle r$).
2. Denser to Rarer (Speeds Up): When light travels from an optically denser to an optically rarer medium, the ray bends away from the normal ($\angle i < \angle r$).
3. Normal Incidence (No Bending): If a ray of light strikes the interface perpendicularly ($\angle i = 0^\circ$), it passes straight into the second medium without any deviation ($\angle r = 0^\circ$).

3. Refraction Through a Rectangular Glass Slab

When a ray of light passes through a parallel-sided glass slab, it undergoes two successive refractions:

                            Incident Ray
                                                                 \ ∠i
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (Air-Glass Interface)
                                  | \ ∠r
                                  |  \ Refracted Ray inside glass
                                  |       ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~+----+~~~~~~~~~~~~~~~~~~~~~~~~~~ (Glass-Air Interface)
                                  |     \ ∠e
                                  |      \ Emergent Ray
                                                               <---- Lateral Displacement d ---->

1. First Interface (Air to Glass): Light enters from rarer air into denser glass $\implies$ bends towards the normal ($\angle i > \angle r$).
2. Second Interface (Glass to Air): Light leaves denser glass into rarer air $\implies$ bends away from the normal by the exact same amount.
3. Emergent Ray Parallelism: Because the two refracting surfaces are parallel, the extent of bending at the opposite faces is equal and opposite: $\mathbf{\text{Angle of Incidence } (\angle i) = \text{Angle of Emergence } (\angle e)}$ The emergent ray is strictly parallel to the incident ray!
4. Lateral Displacement: Although the emergent ray is parallel to the original incident path, it is shifted sideways by a perpendicular distance. This perpendicular distance is called lateral displacement.

4. The Laws of Refraction and Snell's Law

The Two Laws of Refraction:

1. The First Law: The incident ray, the refracted ray, and the normal to the interface of two transparent media at the point of incidence all lie in the same plane.
2. The Second Law (Snell's Law of Refraction):

   The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a light of a given colour and for a given pair of media: $\mathbf{\frac{\sin i}{\sin r} = \text{Constant} = n_{21}}$

This constant value $n_{21}$ is called the refractive index of the second medium with respect to the first medium.

5. The Refractive Index

1. Relative Refractive Index ($n_{21}$):

The refractive index of medium 2 with respect to medium 1 is the ratio of the speed of light in medium 1 ($v_1$) to the speed of light in medium 2 ($v_2$): $\mathbf{n_{21} = \frac{\text{Speed of light in medium 1 } (v_1)}{\text{Speed of light in medium 2 } (v_2)}}$

2. Absolute Refractive Index ($n$):

When medium 1 is vacuum or air, the refractive index of medium 2 is called its absolute refractive index ($n$): $\mathbf{n = \frac{\text{Speed of light in vacuum } (c)}{\text{Speed of light in medium } (v)} = \frac{3 \times 10^8\text{ m/s}}{v}}$

Since speed of light in vacuum is the maximum possible speed in the universe, the absolute refractive index $n$ of any material medium is always greater than 1 ($n > 1$) and has no units (dimensionless ratio).

Selected Absolute Refractive Indices (NCERT Table 9.3):

• Air: $1.0003$
• Water: $1.33$
• Kerosene: $1.44$
• Crown Glass: $1.52$
• Diamond: $2.42$ (Highest optical density among common substances!)

6. Optical Density vs. Mass Density: The Kerosene Paradox

Students often confuse optical density with mass density (mass per unit volume):

• Mass Density: Ratio of mass to volume ($\text{kg/m}^3$).
• Optical Density: The ability of a medium to refract or slow down light.

Important: <u>A medium with higher optical density does NOT necessarily have higher mass density! For example: Kerosene has a LOWER mass density than water (kerosene floats on water), but kerosene has a HIGHER refractive index ($1.44$) than water ($1.33$), making kerosene OPTICALLY DENSER than water!</u>

7. Solved CBSE Board Examination Problems

Solved Example: Speed of Light in Glass

Problem: Light enters from air to glass having a refractive index of $1.50$. What is the speed of light in the glass? (Speed of light in vacuum is $3 \times 10^8\text{ m/s}$).

Solution:

1. Given data:
   • Refractive index of glass $n = 1.50$.
   • Speed of light in vacuum $c = 3 \times 10^8\text{ m/s}$.
2. Apply the absolute refractive index formula: $n = \frac{c}{v} \implies v = \frac{c}{n}$
3. Substitute the values: $v = \frac{3 \times 10^8}{1.50} = \mathbf{2 \times 10^8\text{ m/s}}$
4. Therefore, <u>the speed of light in glass is $2 \times 10^8\text{ metres per second}$</u>.

8. Summary and Examination Tips

Exam Tip: In questions asking "Why does diamond sparkle brilliantly?", state that diamond has an extremely high refractive index of $2.42$, which results in a very low critical angle and causes multiple total internal reflections of light within its cut facets!

Common Mistake: Writing units for refractive index. The refractive index is a pure ratio of two identical quantities (speeds) and has NO UNITS.