Grade 10 Chapter 6: Refraction of Light

Introduction

Refraction of light is one of the most important optical phenomena that explains how light behaves when it passes from one transparent medium to another. This chapter explores the fundamental principles of refraction, its laws, and various applications in our daily lives.

What is Refraction?

Refraction is the bending of light when it passes from one transparent medium to another due to the change in its speed. When light travels from one medium to another, its speed changes, causing it to change direction at the boundary between the two media.

Why Light Bends

Light travels at different speeds in different media. The speed of light is maximum in vacuum (approximately 3 × 10⁸ m/s). When light enters a denser medium from a rarer medium: - Its speed decreases - It bends towards the normal to the boundary - Its wavelength decreases - Its frequency remains constant

Conversely, when light enters a rarer medium from a denser medium: - Its speed increases - It bends away from the normal - Its wavelength increases - Its frequency remains constant

Refractive Index

The refractive index (n) of a medium is a measure of how much the speed of light is reduced in that medium compared to its speed in vacuum.

Mathematically, refractive index is defined as: n = Speed of light in vacuum (c) / Speed of light in the medium (v)

Since the speed of light in any medium is less than or equal to its speed in vacuum, the refractive index of any medium is always greater than or equal to 1.

Absolute and Relative Refractive Index

1. Absolute Refractive Index: The ratio of the speed of light in vacuum to the speed of light in the medium. n = c/v

2. Relative Refractive Index: The ratio of the speed of light in the first medium to the speed of light in the second medium. n₁₂ = Speed of light in medium 1 / Speed of light in medium 2 = n₂/n₁

Refractive Indices of Common Materials

Laws of Refraction

Snell's Law

Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media.

Mathematically: n₁ sin(i) = n₂ sin(r)

Where: - n₁ is the refractive index of the first medium - n₂ is the refractive index of the second medium - i is the angle of incidence - r is the angle of refraction

The First Law of Refraction

The incident ray, the refracted ray, and the normal to the interface at the point of incidence all lie in the same plane.

Optical Phenomena Due to Refraction

Total Internal Reflection

Total internal reflection occurs when light traveling in a denser medium tries to enter a rarer medium at an angle of incidence greater than the critical angle.

The critical angle (C) is the angle of incidence for which the angle of refraction is 90°.

Mathematically: sin(C) = n₂/n₁ (where n₁ > n₂)

Conditions for total internal reflection: 1. Light must travel from a denser medium to a rarer medium 2. The angle of incidence must be greater than the critical angle

Applications of Total Internal Reflection

1. Optical Fibers: Used in telecommunications and medical endoscopy
2. Diamonds: The brilliance of diamonds is due to total internal reflection
3. Prisms: Used in binoculars and periscopes
4. Mirage: A natural phenomenon caused by total internal reflection

Apparent Depth

When an object is placed in a denser medium (like water), it appears to be at a different position when viewed from outside the medium. This is due to refraction.

The apparent depth is related to the real depth by: Apparent depth = Real depth / Refractive index of the medium

Lateral Shift

When light passes through a parallel-sided glass slab, the emergent ray is parallel to the incident ray but laterally displaced. This displacement is called lateral shift.

The lateral shift depends on: - The thickness of the slab - The refractive index of the slab - The angle of incidence

Dispersion of Light

Dispersion is the phenomenon of splitting of white light into its constituent colors when it passes through a prism. This happens because different colors of light have different wavelengths and hence are refracted by different amounts.

The order of colors in the spectrum (VIBGYOR): - Violet (most refracted) - Indigo - Blue - Green - Yellow - Orange - Red (least refracted)

Causes of Dispersion

The refractive index of a medium varies with the wavelength of light. Generally, the refractive index is higher for shorter wavelengths (like violet) and lower for longer wavelengths (like red).

Natural Phenomena Due to Dispersion

1. Rainbow: Formed when sunlight is dispersed by water droplets in the atmosphere
2. Diamond's Fire: The colorful sparkle of diamonds is due to dispersion

Atmospheric Refraction

Atmospheric refraction refers to the bending of light as it passes through the Earth's atmosphere due to the variation in air density with altitude.

Effects of Atmospheric Refraction

1. Twinkling of Stars: Stars appear to twinkle because the light from them passes through layers of atmosphere with varying densities
2. Sunrise and Sunset: The Sun is visible even when it is slightly below the horizon due to atmospheric refraction
3. Apparent Flattening of the Sun: The Sun appears flattened at sunrise and sunset due to differential refraction

Scattering of Light

Scattering is the phenomenon in which light is redirected in multiple directions when it interacts with particles in a medium.

Rayleigh Scattering

Rayleigh scattering occurs when light interacts with particles much smaller than its wavelength. The intensity of scattered light is inversely proportional to the fourth power of the wavelength.

This explains: - Why the sky appears blue (blue light is scattered more) - Why sunsets appear red (red light is scattered less)

Optical Instruments Based on Refraction

Simple Microscope (Magnifying Glass)

A simple microscope consists of a single convex lens with a short focal length. It produces a virtual, erect, and magnified image of an object placed within its focal length.

Compound Microscope

A compound microscope consists of two convex lenses: the objective lens and the eyepiece. It provides much higher magnification than a simple microscope.

Telescope

A telescope is used to view distant objects. The refracting telescope uses two convex lenses to form a magnified image of distant objects.

Practical Applications of Refraction

1. Lenses: Used in eyeglasses, cameras, microscopes, and telescopes
2. Prisms: Used in spectrometers, binoculars, and periscopes
3. Optical Fibers: Used in telecommunications and medical imaging
4. Corrective Eye Surgery: Procedures like LASIK modify the cornea's refractive properties

Experimental Verification of Laws of Refraction

Experiment to Verify Snell's Law

Materials Required: - Glass slab - Drawing board - White paper - Pins - Protractor - Pencil

Procedure: 1. Place a glass slab on a white paper on a drawing board 2. Trace the outline of the glass slab 3. Draw a normal to one of the sides 4. Place pins at different angles of incidence 5. View the pins from the other side and place more pins in line with the refracted rays 6. Remove the glass slab and draw lines connecting the pins 7. Measure the angles of incidence and refraction 8. Calculate the ratio of sin(i) to sin(r) for each set of measurements

Observation: The ratio sin(i)/sin(r) is constant for all angles, verifying Snell's law.

Summary

Refraction of light is a fundamental optical phenomenon that occurs when light passes from one medium to another. It follows Snell's law, which relates the angles of incidence and refraction to the refractive indices of the media. Various optical phenomena like total internal reflection, dispersion, and atmospheric refraction are based on the principles of refraction. Understanding refraction is crucial for explaining natural phenomena and designing optical instruments.

Key Terms

• Refraction
• Refractive index
• Snell's law
• Critical angle
• Total internal reflection
• Dispersion
• Lateral shift
• Apparent depth
• Atmospheric refraction
• Scattering