Unit 14: Light

Normal: A line drawn perpendicular (90°) to the reflecting surface at the point where the incident ray strikes it.

Angle of Incidence (i): The angle between the incident ray and the normal at the point of incidence.

Angle of Reflection (r): The angle between the reflected ray and the normal at the point of reflection.

Law of Reflection: The incident ray, the normal, and the reflected ray all lie in the same plane, and the angle of incidence is equal to the angle of reflection (i = r).

Critical Angle: The angle of incidence for which the angle of refraction is 90° is called the critical angle.

Total Internal Reflection (TIR): Total internal reflection is the phenomenon of reflection of light ray back to the same medium when passing from denser medium to rarer medium in such a way that angle of incidence is greater than its critical angle.

Conditions Required for Total Internal Reflection:
i. Light must travel from a denser medium to a rarer medium (higher refractive index to lower refractive index).
ii. The angle of incidence must be greater than the critical angle (i > C).

Assumptions:
i. Light travels from a denser medium (refractive index n₁ = n) to air (refractive index n₂ = 1).
ii. The angle of incidence is exactly equal to the critical angle (i = C).

Derivation: To derive a formula for total internal reflection, we start with Snell's law:

\[ n_1 \sin i = n_2 \sin r \]

Substitute the given conditions into the equation:
• Let n₁ = n (refractive index of the denser medium)
• Let n₂ = 1 (refractive index of air)
• Set the angle of incidence i = C (critical angle)
• By definition of the critical angle, the angle of refraction r = 90°

\[ n \sin C = 1 \sin 90° \]
\[ n \sin C = (1)(1) \]
\[ n \sin C = 1 \]
\[ n = \frac{1}{\sin C} \]

Finding the Critical Angle: if we have to find critical angle, then

\[ \sin C = \frac{1}{n} \]
\[ C = \sin^{-1} \left( \frac{1}{n} \right) \]

Note: These relations are valid when light travels from a denser medium to air (or vacuum). More generally, if light travels from a medium of refractive index n₁ to another medium of refractive index n₂, then

\[ C = \sin^{-1} \left( \frac{n_2}{n_1} \right) \]

An optical fibre is a very thin, flexible strand made of high-quality glass or plastic that transmits light signals.

It consists of two main parts:

Core: The central inner cylinder made of glass or plastic with a higher refractive index. Light signals travel inside this core.

Cladding: An outer layer surrounding the core, made of glass or plastic with a lower refractive index.

This difference in refractive indices allows total internal reflection to keep the light contained inside the core.

Two Advantages of Optical Fibres: Compared to traditional copper cables, optical fibres offer several key benefits:

i. High Bandwidth: Optical fibres can carry a much larger amount of data than copper wires. Bandwidth means how much data can be sent over a network per second. In today's world, where we need fast internet, optical fibres are the best choice because they support high-speed data transfer.

ii. Low Power Consumption: They use less power than copper cables. Also, because they last longer and are more durable, they reduce the cost of repairs and maintenance.

iii. Faster Speed: They send data using light pulses, which travel extremely fast almost at the speed of light.

iv. Long Distance Transmission: Optical fibres can carry data across very long distances without losing signal quality.

v. Resistance to Electrical Interference: Since optical fibres use light instead of electricity, they are not affected by electrical noise or interference.

In long-sightedness, a person can see distant objects clearly, but nearby objects appear blurry.

Causes of Long-sightedness: This happens when the eye lens is too weak or the eyeball is too small, so the light rays from near objects are not bent enough. As a result, the rays focus behind the retina instead of on it.

There are two main causes:

i. Lens too weak: The lens does not bend the light rays enough.

ii. Eyeball too small: The retina is too close to the lens.

In both cases, the image is formed behind the retina, making close-up vision blurry.