Snell's Law Explained: Incidence and Refraction

Snell's law is a fundamental principle in optics that describes the relationship between the direction of light and its speed as it passes through the boundary between two different isotropic media. This phenomenon is known as refraction.

Defining the Angles

In the context of Snell's law:

• The angle of incidence (denoted by i) is the angle between the incoming light ray and the normal (an imaginary line perpendicular) to the surface at the point of incidence.
• The angle of refraction (denoted by r) is the angle between the refracted light ray (the ray after passing through the boundary) and the normal.

Snell's Law Formula

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 any given pair of media. Mathematically, it is expressed as:

$ n_1 \sin i = n_2 \sin r $

Where:

• n₁ is the refractive index of the first medium (where the light is coming from).
• n₂ is the refractive index of the second medium (where the light is entering).
• i is the angle of incidence.
• r is the angle of refraction.

Deriving the Correct Relation

To find the relationship asked in the question, we can rearrange Snell's law formula:

$ \frac{\sin i}{\sin r} = \frac{n_2}{n_1} $

For a specific pair of transparent media (like air and water, or glass and water), their refractive indices (n₁ and n₂) are constant values. Therefore, the ratio $\frac{n_2}{n_1}$ is also a constant.

This directly leads to the conclusion that:

$ \frac{\sin i}{\sin r} = \text{constant} $

Analyzing the Options

Based on the derived formula:

• Option 1: `sin i ÷ sin r = constant` - This matches our derivation from Snell's law.
• Option 2: `sin i x sin r = constant` - This is incorrect.
• Option 3: `sin i + sin r = constant` - This is incorrect.
• Option 4: `sin i - sin r = constant` - This is incorrect.

Thus, the correct relation according to Snell's law is that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.