**Snell’s law** describes the relationship between the angles of incidence and refraction when a light wave passes from one medium into another with a different refractive index. According to Snell’s law, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant and is equal to the ratio of the refractive indices of the two media. This law is fundamental in understanding how light bends, or refracts, when it enters a different medium. For example, when light passes from air (with a refractive index of approximately 1) into water (with a refractive index of about 1.33), it bends towards the normal due to the change in speed of light in the two different media.

Snell’s law is mathematically expressed as:

$$n_{1}sin\theta_{1} = n_{2}sin\theta_{2}$$where n_{1} and n_{2} are the refractive indices of the first and second media, respectively, and θ_{1} and θ_{2} are the angles of incidence and refraction, respectively.

## Practice problems

### Problem #1

A ray of light moving through medium 1 with a refractive index of 1 enters medium 2 with a refractive index of 1.33. If the angle of incidence is 30°, what is the angle of refraction?

**Solution**

Given data:

- Refractive index of medium 1, n
_{1}= 1 - Refractive index of medium 2, n
_{2}= 1.33 - Angle of incidence, θ
_{1}= 30° - Angle of refraction, θ
_{2}= ?

Applying the formula:

- n
_{1}sin θ_{1}= n_{2}sin θ_{2} - 1 × sin (30°) = 1.33 × sin θ
_{2} - 1 × 0.5 = 1.33 × sin θ
_{2} - 0.5 = 1.33 × sin θ
_{2} - sin θ
_{2}= 0.3759 - θ
_{2}= sin^{-1}(0.3759) - θ
_{2}= 22.07°

Therefore, the angle of refraction is **22.07°**.

### Problem #2

A laser beam traveling through medium 1 has an angle of incidence of θ_{1} = 40° and a refractive index of n_{1} = 1.33. If the angle of refraction is θ_{2} = 45°, calculate the refractive index of medium 2.

**Solution**

Given data:

- Angle of incidence, θ
_{1}= 40° - Refractive index of medium 1, n
_{1}= 1.33 - Angle of refraction, θ
_{2}= 45° - Refractive index of medium 2, n
_{2}= ?

Applying the formula:

- n
_{1}sin θ_{1}= n_{2}sin θ_{2} - 1.33 × sin (40°) = n
_{2}× sin (45°) - 1.33 × 0.6427 = n
_{2}× 0.7071 - n
_{2}= 0.8547 ÷ 0.7071 - n
_{2}= 1.20

Therefore, the refractive index of medium 2 is **1.20**.

### Problem #3

A ray traveling through medium 1 with a refractive index of n_{1} = 1.3 enters medium 2 with a refractive index of n_{2} = 1.4. Calculate the angle of incidence if the angle of refraction is 25°.

**Solution**

Given data:

- Refractive index of medium 1, n
_{1}= 1.3 - Refractive index of medium 2, n
_{2}= 1.4 - Angle of incidence, θ
_{1}= ? - Angle of refraction, θ
_{2}= 25°

Applying the formula:

- n
_{1}sin θ_{1}= n_{2}sin θ_{2} - 1.3 × sin θ
_{1}= 1.4 × sin (25°) - 1.3 × sin θ
_{1}= 1.4 × 0.4226 - 1.3 × sin θ
_{1}= 0.5916 - sin θ
_{1}= 0.5961 ÷ 1.3 - sin θ
_{1}= 0.4585 - θ
_{1}= sin^{-1}(0.4585) - θ
_{1}= 27.29°

Therefore, the angle of incidence is **27.29°**.

### Problem #4

A light traveling through medium 1 with an unknown refractive index enters medium 2 with a refractive index of n_{2} = 1.2. If the angle of incidence is 20° and the angle of refraction is 35°, what is the refractive index of medium 1?

**Solution**

Given data:

- Refractive index of medium 2, n
_{2}= 1.2 - Angle of incidence, θ
_{1}= 20° - Angle of refraction, θ
_{2}= 35° - Refractive index of medium 1, n
_{1}= ?

Applying the formula:

- n
_{1}sin θ_{1}= n_{2}sin θ_{2} - n
_{1}× sin (20°) = 1.2 × sin (35°) - n
_{1}× 0.3420 = 1.2 × 0.5735 - n
_{1}× 0.3420 = 0.6882 - n
_{1}= 0.6882 ÷ 0.3420 - n
_{1}= 2.01

Therefore, the refractive index of medium 1 is **2.01**.

## More topics

- Law of conservation of energy
- Newton’s law of universal gravitation
- Newton’s law of cooling
- Coulomb’s law
**Snell’s law**- Ohm’s law
- Hooke’s law

## External links

- https://www.britannica.com/science/Snells-law
- https://www.physicsclassroom.com/class/refrn/Lesson-2/Snell-s-Law
- https://www.omnicalculator.com/physics/snells-law
- https://study.com/learn/lesson/what-is-snells-law-equation-examples.html
- https://www.studysmarter.us/explanations/physics/waves-physics/snells-law/

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.