How Does Snell's Law Explain the Bending of Light?
Snell's Law, also known as the Law of Refraction, is a principal concept in optics that describes the change in direction of light as it passes from one medium to another. This bending of light explains many everyday phenomena and is vital for the construction and understanding of optical devices such as lenses, prisms, and microscopes.
When a light ray moves from one transparent medium (like air) into another (like water or glass), its speed changes, causing the ray to change direction at the boundary. This change is known as refraction.
Understanding the Law of Refraction
The Law of Refraction establishes a consistent mathematical relationship between the angles and the speed of light in different media. When light travels from one medium into another with a different optical density, its path bends at the interface. This is represented by Snell’s Law.
Snell’s Law can be summarized as: the ratio of the sine of the angle of incidence (in the first medium) to the sine of the angle of refraction (in the second medium) remains constant and is equal to the ratio of the refractive indices of the two media.
Snell’s Law Formula
The mathematical form of Snell's Law is given as:
Where:
- n1: Refractive index of the first medium
- n2: Refractive index of the second medium
- θ1: Angle of incidence (with respect to the normal)
- θ2: Angle of refraction (with respect to the normal)
Example of Refraction with Data
Tables of refractive indices help illustrate how much the speed of light changes between substances. For instance, common refractive indices for light of wavelength 600 nm are:
| Substance | Refractive Index, n |
|---|---|
| Air (1 atmosphere, 0°C) | 1.00029 |
| Water (20°C) | 1.33 |
| Crown Glass | 1.52 |
| Flint Glass | 1.66 |
These values indicate that light travels fastest in air, slower in water, and slowest in flint glass. The difference in speed causes bending, which Snell's Law precisely quantifies.
Interpreting Snell’s Law with an Example
Suppose a light ray in air (n = 1.00029) enters water (n = 1.33) at a certain angle. Due to the higher refractive index of water, the ray bends towards the normal (the perpendicular to the boundary at the point of incidence).
Snell’s Law allows you to calculate the new angle in the water if the entry angle in air is known. For example, if the angle of incidence in air is θ1, the angle in water θ2 can be found using:
Physically: Why the Bending?
The bending of light, or refraction, happens because light changes speed when moving between media with different refractive indices. A higher refractive index means the light travels slower, and bends more noticeably.
If a light ray passes from air into crown glass, it will bend more than when passing from air into water. Snell’s Law lets you predict both the degree and direction of this bending.
Parallel Light Beams and Refraction
After passing through parallel-sided mediums, such as a slab of glass, the emerging light beam is parallel to the incident beam. This demonstrates that although the beam is laterally displaced inside the medium, its direction after exiting is unchanged with respect to the original path.
This fact is a direct outcome of Snell’s Law and is observed in experiments involving glass slabs and other transparent materials.
Stepwise Approach for Solving Snell’s Law Problems
- Identify the indices of refraction (n1, n2) for each medium.
- Determine the angle of incidence θ1.
- Apply the formula: n1 sin θ1 = n2 sin θ2.
- Solve for θ2 using sin-1 if needed.
Key Formulas Table
| Formula | Usage |
|---|---|
| n1 sin θ1 = n2 sin θ2 | Finding angle after refraction |
Applications of the Law of Refraction
- Understanding how lenses bend light in devices such as microscopes and telescopes.
- Predicting the path of light in fiber optics for information transfer.
- Explaining natural phenomena, for example, why objects appear bent in water.
- Essential for solving problems in refraction and lenses.
Further Study and Practice on Refraction
FAQs on Snell's Law of Refraction: Meaning, Formula, and Uses
1. What is Snell's law of refraction?
Snell's law of refraction states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for the given pair of media. Mathematically, it is expressed as: n1sin i = n2sin r, where n1 and n2 are the refractive indices of the two media, i is the angle of incidence, and r is the angle of refraction.
2. State the law of refraction.
The law of refraction, also called Snell's Law, states that the ratio of the sin of the angle of incidence (i) to the sin of angle of refraction (r) is constant for light traveling between two specific optical media. This constant is the ratio of their refractive indices. Mathematically: n1sin i = n2sin r.
3. What is the formula for Snell's law of refraction?
The formula for Snell's law of refraction is:
n1sin i = n2sin r
where:
- n1 = Refractive index of medium 1
- n2 = Refractive index of medium 2
- i = Angle of incidence
- r = Angle of refraction
4. What is the significance of Snell's law in daily life?
Snell's law explains many everyday optical phenomena.
Examples include:
- The apparent bending of a straw in water
- The design and working of lenses in eyeglasses and cameras
- Mirages observed on hot roads
- The apparent depth of swimming pools and lakes
5. What are the refractive indices of some common substances?
Typical refractive indices (approximately):
- Air: 1.00029
- Water: 1.33
- Crown Glass: 1.52
- Flint Glass: 1.66
These values can be used in Snell's law calculations to determine angles of refraction.
6. What is critical angle and how is it related to Snell’s law?
Critical angle is the angle of incidence in a denser medium for which the angle of refraction in the rarer medium becomes 90°. It is derived using Snell’s law: sin C = n2/n1, where C is the critical angle, n1 is the refractive index of the denser medium, and n2 is that of the rarer medium.
7. What do n1 and n2 represent in Snell's law?
In Snell's law:
- n1 is the refractive index of the medium where the incident ray travels.
- n2 is the refractive index of the medium where the refracted ray travels.
Higher refractive index means the medium is optically denser.
8. Where does Snell's law not apply?
Snell’s law may not apply when:
- Light passes through non-homogeneous or non-transparent media
- The boundary surface is rough or absorbing
- At total internal reflection (when the angle of incidence exceeds the critical angle for a denser to rarer medium transition), no refraction occurs
- In cases involving very high light intensities (nonlinear optics)
9. Who discovered Snell's law?
Snell's law was discovered by the Dutch mathematician and astronomer Willebrord Snellius (also called Snell) in 1621.
10. How do you derive Snell's law?
Snell’s law is derived using the wave theory of light and the principle of least time (Fermat’s Principle).
Steps:
1. Consider a light wave passing from one medium to another at an interface.
2. Using the difference in speeds of light between the two media and applying Fermat’s principle, derive the relationship n1sin i = n2sin r.
11. What is the difference between reflection and refraction?
Reflection occurs when light bounces back from a surface; refraction is the bending of light as it passes from one medium to another.
- Reflection: No change in medium, follows law of reflection.
- Refraction: Change in medium and direction, follows Snell’s law of refraction.
12. Give one solved numerical example using Snell’s law.
Example: Light passes from air (n=1) into water (n=1.33) at an angle of incidence 30°.
Solution:
- n1 = 1; n2 = 1.33; i = 30°
- By Snell’s law: n1sin i = n2sin r
- sin r = (1/1.33) × sin 30° = 0.3759
- r = arcsin(0.3759) ≈ 22°
Therefore, angle of refraction ≈ 22°.
