Refraction of Light

Refraction is the bending of light as it passes from one medium to another. This bending occurs due to a change in the speed of light in different media.

When a ray of light travels from an optically less dense medium (e.g., air) to an optically dense medium (e.g., water, glass), it bends towards the normal. Conversely, a ray passing from a denser medium to a less dense medium bends away from the normal.

Laws of Refraction

The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane.
The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media.

This second law is known as Snell’s Law:

\[ n = \frac{\sin i}{\sin r} \]

where \( n \) is the refractive index of the second medium relative to the first.

For light traveling from air to glass:

\[ n_g = \frac{\sin i}{\sin r} \]

Using the principle of reversibility:

\[ n_g = \frac{1}{n_{ag}} \]

Also, refractive index can be expressed as:

\[ n = \frac{\text{speed of light in medium }}{\text{speed of light in medium }} \]

Effects of Refraction

The bottom of a clear river or pond appears shallower than it really is.
A rod or spoon appears bent or broken when partially immersed in water.
Printed letters appear raised when a thick block of glass is placed over them.

Refraction Through a triangular Prism

The refractive index \( n \) is given by:

\[ n = \frac{\sin \left( \frac{A}{2} + \frac{D}{2} \right)}{\sin \frac{A}{2}} \]

Total Internal Reflection & Critical Angle

When light passes from a denser to a less dense medium, it can experience total internal reflection if the angle of incidence exceeds the critical angle \( C \).

At the critical angle:

\[ \text{angle of refraction} = 90^\circ \]

For incidence angles greater than \( C \), all the light is reflected back into the denser medium.

An example of total internal reflection is a mirage on a road, where light is bent due to varying air densities.

Real and Apparent Depth

When viewed from above, a thick glass slab appears about two-thirds of its actual thickness. Similarly, water in a pond appears about three-quarters of its real depth.

The refractive index is given by:

\[ n = \frac{\text{real depth}}{\text{apparent depth}} \]

Dispersion of White Light

White light consists of a range of wavelengths corresponding to different colors. This band of colors is known as the spectrum of white light.

The phenomenon of dispersion was first discovered by Sir Isaac Newton in 1666 at Cambridge. He conducted an experiment by allowing a small beam of light to enter a dark room through a circular opening in a shutter. A prism was placed near the hole, causing the light to refract and spread onto the opposite wall. The colors appeared in the following order:

Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV)

This experiment demonstrated that a prism can separate or disperse white light into its individual colors or wavelengths. Dispersion occurs because different colors travel at different speeds through glass, causing them to bend at different angles.

Production of a Pure Spectrum

To produce a pure spectrum, a converging lens is placed between the light source and the prism, ensuring that the distance between the source and the lens is equal to its focal length. Another lens is positioned between the prism and the screen to focus the dispersed colors. This setup ensures that a clear and distinct spectrum is projected onto the screen.

Color Mixing

All visible colors can be created by combining three basic colors known as primary colors: red, blue, and green.

Mixing two primary colors produces a secondary color:

Red + Blue = Magenta
Red + Green = Yellow
Blue + Green = Cyan

Combining all three primary colors results in white light. This process is called additive mixing and is the basis for color display technology, including color movies and digital screens.

Coloured Filters and Pigments

Coloured filters are made from tinted glass or plastic and work by transmitting only their own color while absorbing all others.

Objects are visible because they reflect light into our eyes. The substance responsible for an object's color is called a pigment. A pigment absorbs all colors except its own, which it reflects.

A black pigment absorbs all colors and reflects none.
A white pigment reflects all colors.

Pigments, such as those used in paints, can also be mixed to create different colors. This process is known as subtractive mixing.