Refraction of light — KCSE Physics

Snell's law describes how light refracts when it passes from one medium to another. It is mathematically expressed as:

n = sin i / sin r

Where:

• n = refractive index of the medium
• i = angle of incidence (angle between the incoming ray and the normal)
• r = angle of refraction (angle between the refracted ray and the normal)

To use Snell's law, follow these steps:

1. Identify the angles of incidence and refraction.
2. Use the formula to calculate the unknown variable (n, i, or r).

Example: Calculate the refractive index when the angle of incidence is 30° and the angle of refraction is 22°.

Solution:

• Given: i = 30°, r = 22°
• Using Snell's law:

n = sin(30°) / sin(22°)

n = 0.5 / 0.3746 ≈ 1.34

Thus, the refractive index is approximately 1.34.

The critical angle is defined as the angle of incidence in a denser medium at which light is refracted at an angle of 90 degrees in the less dense medium. When the angle of incidence exceeds this critical angle, total internal reflection occurs, meaning all the light is reflected back into the denser medium, with no refraction. This phenomenon is crucial in optical fibers and prisms.

To calculate the critical angle (c), we use the formula:

[ \sin(c) = \frac{1}{n} ]

where n is the refractive index of the denser medium. For example, if light travels from water (n = 1.33) to air (n = 1.00), we can find the critical angle as follows:

1. Substitute n into the formula: ( \sin(c) = \frac{1}{1.33} )
2. Calculate: ( \sin(c) \approx 0.7519 )
3. Find c: ( c \approx 48.6^{\circ} )

Thus, the critical angle for water to air is approximately 48.6 degrees.

Total internal reflection occurs when light travels from a denser medium to a less dense medium at an angle greater than the critical angle. This principle has several important applications:

• Optical Fibres: Used in telecommunications, optical fibres transmit light signals over long distances with minimal loss. The light reflects internally, allowing for efficient data transmission.
• Periscopes: Utilized in submarines, periscopes use total internal reflection to allow users to see above the water's surface while remaining submerged. Mirrors positioned at 45-degree angles reflect light down the tube.
• Binoculars: Binoculars enhance distant vision by using prisms that employ total internal reflection. This allows for a compact design while providing a correct image orientation.
• Sparkling of Diamonds: Diamonds exhibit brilliance due to total internal reflection. The cut of the diamond ensures that light entering it reflects multiple times, creating a sparkling effect.

Understanding these applications illustrates the practical significance of total internal reflection in technology and nature.