Refraction is the bending of light when it travels from one medium to another due to a change in its speed.
The laws of refraction of light describe how light bends when it passes from one medium (like air) to another (like water or glass).
Laws of Refraction of Light are:-
1. First Law of Refraction of Light
It states that the incident ray, refracted ray, and normal to the interface at the point of incidence all lie in the same plane.
2. Second Law of Refraction of Light
It states that the ratio of the sine of the angle of incidence (i) and the sine of the angle of refraction (r) is constant. It is given as,
\frac{\sin i}{\sin r} = \mu = \text{Constant}
Snell's Law
The second Law of Refraction of Light is also called Snell's Law. According to Snell's Law, for the light if given color and for the given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. It gives the degree of refraction and also tells the relation between the angle of incidence, the angle of refraction, and the refractive index of media.
\bold{\frac{\sin i}{\sin r} = \mu = \text{Constant}}
Note: One point point to remember is that light has dual nature, i.e. it behove both as Wave and Particle. The phenomena that show the wave nature of light is Refraction of Light, Reflection of Light, polarization of Light, etc. And particle nature of light is shows using Photoelectric Effect, etc.
Real World Observation
1. When we put a pencil in a glass of water, we observe that the pencil appears slightly bent, but it is actually straight.
2. On a hot summer day, we often notice the sudden appearance of water in the middle of the road, only to find that there is nothing when we approach nearer to it.
Solved Examples
Example 1: The refractive index of air to water is 5/3. The angle of incidence is sin 50°. Find the angle of refraction.
Solution: Given,
- i = 50°
- μ = 5/3
Since,
μ = sin 50°/ sin r
sin r = sin 50° × (3/5)
= 0.766 × (3/5)
= 0.4596r = sin-1(0.4596)
= 27.36°
Therefore, the angle of refraction will be 27.36°.
Example 2: The velocity of light in glass is 2 × 108m/s and the velocity of light in air is 3 × 108m/s. Find the refractive index of glass.
Solution: Given,
- v = 2 × 108 m/s
- c = 3 × 108 m/s
Since,
μ = c/v
Therefore,
μ = 3 × 108/ 2 ×108
= 1.5
Therefore, refractive index will be 1.5
Example 3: Light travelling through an optical fiber (n = 1.45) is incident at the end of the fiber at 30°. Determine the angle of refraction beyond the fiber.
Solution: Given,
- Refractive Index of the Fiber, μ is 1.45
- Angle of Incidence, ∠i is 30°.
Since,
μ1 × sin i = μ2 × sin r
1.45 × sin 30° = 1 × sin r
1.45 × 1/2 = sin r
r = sin-1(0.725)
r = 46.46°
Thus, the required angle of refraction is, 46.46°
Example 4: Consider a ray that is refracted at an angle of 20° and the refractive index is 1.5. Determine the angle of incidence by the ray.
Solution: Given,
- Refractive Index, μ is 1.5
- Angle of Refraction, ∠r is 20°
Since,
μ = sin i / sin r
1.5 = sin i / sin 20°
sin i = 0.513
i = sin-1(0.513)
i = 30.86°
Thus, the required angle of incidence is, 30.86°
Unsolved Problems
Q1: The refractive index of material is 1.25 what is the speed of light in it?
Q2: If the light travels in a medium with the speed of 2 ⨯ 108 m/s, then what is the refractive index of the medium?
Q3: If the angle of incidence is 45° and the angle of refraction is 30°, then what is the refractive index of the medium?
Q4: Predict whether the medium is denser or rarer if the angle of incidence is 60° and the angle of refraction is 30°.