Refraction of Light

1. Angle of incidence (i): The angle between the incident ray and the normal at the point of incidence.
2. Angle of refraction (r): The angle between the refracted ray and the normal.

1. First law: The incident ray, the refracted ray, and the normal all lie in the same plane.
2. Second law (Snell's law):

$\frac{\sin i}{\sin r} = \text{constant (refractive index, } n \text{)}$

• Mathematical definition:

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

• Alternative definition using velocity:

$n = \frac{\text{Velocity of light in air (} V_a \text{)}}{\text{Velocity of light in medium (} V_m \text{)}}$

• Refractive indices of some materials:

Given:

• Refractive index from air to water = 1.333

To find:

• Refractive index from water to air

$n_{wa} = \frac{1}{n_{aw}} = \frac{1}{1.333} = 0.75$

• Real depth: The actual depth of an object in a medium.
• Apparent depth: The depth at which the object appears to be when viewed from above due to refraction.

• Critical angle: The angle of incidence for which the angle of refraction is 90°.
• Formula:

$\sin C = \frac{1}{n} \quad \text{or} \quad C = \sin^{-1} \left( \frac{1}{n} \right)$

Total internal reflection occurs when:

1. Light moves from a denser to a less dense medium.
2. The angle of incidence is greater than the critical angle.

Very thin transparent fibers (plastic or glass) that use total internal reflection to transmit light efficiently.

Uses:

• In telecommunications to transmit data signals.
• In medical endoscopes to view internal organs.

A mirage is an optical illusion caused by the refraction of light in layers of air with different temperatures, commonly observed on hot days when the ground heats the air above it.