What is Refraction of Light?

Refraction is a change in the direction of light rays when they travel from one medium to another. It is the bending of light when it goes through different media.

To understand refraction, we also need to understand similar concepts, like light waves and reflection. Here, we'll review these concepts and discuss the laws of refraction, what causes refraction, and real-world applications of the refraction of light.

What is Light?

Light is electromagnetic radiation. It can be detected by the human eye or animal eye. Visible light is electromagnetic radiation with a wavelength of 400nm to 700nm, between the infrared (IR) region and the ultraviolet (UV) region. Light can behave as a wave (interference and diffraction) or a particle (photoelectric effect).

When visible light is inclined on the interface between the two mediums, it can be reflected back or refracted into the medium.

Reflection of a Light Waves

When visible light rays hit a polished plane surface, the light waves get reflected, or bounce back. These bounced waves are called reflected waves.

Laws of Reflection

• The incident ray, reflected ray, and the plane mirror are three axes in the same plane.
• The angle of reflection is equal to the angle of incidence. The incident and reflected angles are measured with respect to the normal line, which is perpendicular to the plane of the mirror.

The angle of the incident beam (Ө_i)=angle of reflected beam (Ө_r)

Refraction of a Light Waves

Refraction is a change in the direction of light rays when they travels from one medium to another. It is the bending of light when it goes through different media.

The refraction of light is one of the vital occurrences of waves. Refraction is also experienced by both sound waves and water waves. Due to the refraction of light, we have been able to invent optical instruments like magnifying glasses, prisms, and lenses.

${\theta }_i={\theta }_r$

Laws of Refraction

• The incident ray, refracted ray, and the normal line to the surface of two transparent mediums at the point of the incident all lie on the same plane.
• The ratio between the sine of the angle of the incident beam and the sine of the angle of refraction is constant. This is known as Snell’s law of refraction.

$\frac{\sin i}{\sin r}=\mu$

Here,  μ is a constant.

Snell-Descartes Law

Snell’s law is a concept that is used to describe the relationship between the angle of incidence and the angle of reflection. Snell's law is used when light passes from one media to another (like water, air, or glass).

Snell’s law states that the ratio of the sine of the angle of incidence and sine of the angle of reflection is equal to the ratio of phase velocity of light in two media. The ratio is also equal to the reciprocal of the ratio of refractive indices of the two media.

The Snell-Descartes law is expressed as:

$n_1\sin {\theta }_1=n_2\sin {\theta }_2$   

$\frac{n_1}{n_2}=\frac{\sin {\theta }_2}{\sin {\theta }_1}$      

$\frac{n_1}{n_2}=\frac{v_2}{v_1}=\frac{\sin {\theta }_2}{\sin {\theta }_1}$

Where,

${\theta }_1$ is the incident angle measured by the normal boundary.

${\theta }_2$ is the refracted angle measured by the normal boundary.

v₁ and v₂ are the velocities of the light waves (m/s).

n₁ is the incident index.

n₂ is the refractive index.

Fermat’s Theorem

In optics, light waves travel between two points following a path such that the number of waves (the optical lengths between the points) is equal to the first approximation to that neighboring path.

Why Does Refraction Occur?

The frequencies of light remain stable when the light rays are incident on the interface of two mediums, but light travels at different speeds in different media.

$c=\nu \lambda$

As the result, the wavelength of light changes at the interface. Due to this behavior, it causes a directional change, which is called refraction. During refraction, the frequency and wavelength of the light do not remain the same.

Cause of Refraction

Due to Changes in Speed, the Direction Also Changes

Whenever a light ray refracts, it travels at an angle with a medium of various refractive index. This speed changes, resulting in a directional change.

For example, let us consider the sea. Light rays travel above the sea at a higher speed. When they hit the water, the speed of the light rays is decreased, causing them to travel at a different angle.

Refraction of light is shown in the above figure. When light rays travel from air into glass, the waves slow down and change their direction. When light travels from a thin (or less dense) medium to a thick (or higher-density) medium, the refracted waves are bent toward the normal plane.

Suppose a light ray reaches the boundary in the direction that is perpendicular to it. In this case, the light waves do not refract, even though the speed of the light waves change.

Refractive Index of the Medium

The refractive index is used to describe the speed with which light travels through a medium. It is also called an index of refraction. A refractive index is a dimensionless unit.

For a given material, the index of refraction is the ratio between the speed of light waves in a vacuum (empty space) and the speed of light waves in a medium (v). The index of refraction of the medium is described by n.

The refractive index can be derived as,

$n=\frac{c}{v}$

Where,

n is the refractive indexes of the material (always greater than or equal to 1).

c is the speed of light in a vacuum.

v is the speed of light in the medium.

Refractions of Light Waves in Our Daily Life

• Mirages are optical illusions caused by the refraction of light waves.
• Swimming pools always look shallower because light rays reflected from the bottom of the pool bend at the surface due to the refraction of light rays.
• Rays from the sun bend through the raindrops in the clouds due to the refraction of light, forming a rainbow.
• When visible light rays pass through a prism, they splits into multiple colors.

Instruments that Use Refraction of Light

Refraction plays a vital role in optical technology. Some important applications are listed below:

Lens

A lens is a magnifying piece of transparent glass or transparent plastic with a curved surface for concentrating and dispersing the light rays when they pass through by refraction. Due to this magnifying property, lenses are widely used in optical instruments. These lenses are classified into two types:

• Biconvex or converging lenses
• Biconcave or diverging lenses

Converging Lens

In a converging lens, the middle portion is thicker and the edges are thinner. These lenses are used as magnifying glasses, and parallel light rays are focused at a focal point. Each and every light beam that enters into a converging lens refracts or bends toward it. This is continuous until the beam leaves from the lens. 

Diverging Lens

In a diverging or biconcave lens, the middle portion is thinner and the edges are thicker. When light rays enter into this type of lens, they are refracted outward.

Prism

Newton performed experiments using a transparent triangular-shaped glass block called a prism. He found that when sunlight passed through the prism, the prism refracted the light beams into different wavelengths, called vibgyor. Red light has the highest wavelength and violet has the lowest wavelength.

Formulas

The Snell-Descartes law is expressed as,

$n_1\sin {\theta }_1=n_2\sin {\theta }_2$      

$\frac{n_1}{n_2}=\frac{\sin {\theta }_2}{\sin {\theta }_1}$

The refractive index can be derived as,

$n=\frac{c}{v}$

Context and Applications

This topic is important in all forms of classical mechanics and is significant for both undergraduate and postgraduate courses, especially for bachelors and masters in science (physics).

Practice Problems

1. A light wave is traveling in the medium of air and enters into an optical fiber having an index of refraction of 1.44. If the angle of incidence on the end of the optical fiber is 20°, then what is the angle of refraction?

a. $24°$                   
b. $13°$
c. $32°$                   
d. $15°$

Answer: b

Explanation:

Given data:

Refractive index of air medium (n₁) = 1.00

Refractive index of optical medium (n₂) = 1.44

Angle of incident (${\theta }_1$) = 20°

• The light beams travel from the air medium (less dense medium) to the optical medium (denser medium), causing the refracted rays to bend toward the normal line.
• Now let us consider the air medium is n₁ and the optical fiber medium is n₂.

The refracted angle is expressed by,

$n_1\sin {\theta }_1=n_2\sin {\theta }_2$

$(1.00)(\sin 20°)=(1.44)\left(\sin {\theta }_2\right)$

$\sin {\theta }_2=\frac{\sin (20°)}{1.44}$              

$\sin {\theta }_2=\frac{0.3420}{0.6944}$                  

${\theta }_2={\sin }^{-1}(0.2374)$                 

${\theta }_2=13°$

Therefore, the angle of refractions is 13º.

2. The angle of incidence for a ray of light having 0° reflection angle is ___.

a. 14°
b. 0°
c. 20°
d. 30°

Answer: b

Explanation: The laws of reflection state that the angle of reflection is equal to the angle of incidence. The incident and reflected angles are measured with respect to their normal plane mirror.

The angle of the incident beam (Ө_i) = Angle of reflected beam (Ө_r)

3. As light waves travel from a thinner medium to a denser medium, _______.

a. Both velocity and wavelengths increase
b. Both velocity and wavelengths decrease
c. Velocity decreases
d. Wavelength decreases

Answer: b

Explanation: When light waves travel from a thinner medium to a denser medium, its frequency remains constant but the wavelength decreases. Due to the change in wavelength, the velocity of the light waves decreases.

4. Refraction occurs ________ .

a. Only with light waves
b. When there is more than one reflection
c. Due to a change in the speed of a wave
d. None of the above

Answer: c

Explanation: Refraction is caused due to a change in the speed of light. When the light waves passes from an air medium to a water medium, the rays bend towards the normal line due to the reduction of speed.

5. A beam of light travels faster in which medium?

a. Water
b. Air
c. Plastic
d. Glass

Answer: b

Explanation: Light rays travel faster in air compared to other mediums because the density of other mediums, like water, is greater than the density of air. Due to the lower density, light rays travel faster in the air.