Path of Ray of Light Through Prism for JEE

An optical prism is a transparent item that is often composed of glass. The term "prism" refers to a geometric prism with three rectangular lateral surfaces and two triangular bases, which is shaped like a pyramid and has an angle known as the prism angle.

The angle of the prism, also referred to as the refracting angle, is the angle formed by any two of the prism's refracting surfaces with one another. The refracting angle for an equilateral prism is an acute angle of sixty degrees. White light is split into a spectrum of colours when it passes through a prism, which has refracting surfaces. This process is known as dispersion of light.

What is Refraction of Light?

Refraction is the phenomenon in which there is a change in the direction of a wave or a propagation of light when passing from one medium to another due to its change in speed.

Simply put, when light is made to move from one medium to another, the density of the different media affects its speed, which causes it to slow down and change its direction. As a result, as light travels through the prism glass from the air, its speed varies as a result of the glass's and air's different refraction indexes, which causes the light to bend.

Refraction is a typical phenomenon that we see everyday. Examples include rainbows, mirages, and twinkling of stars as a result of light refracting through the layers of the atmosphere.

Path of Ray of Light through Prism

• A light beam (PE) travelling through the air strikes the face AB of a triangular glass prism ABC, where it is refracted and bent in the direction of the plane of the face AB. 

• Until it hits the other face AC of the prism, the refracted ray EF travels inside the prism. Once more, the beam from the glass is refracted into the air but bends in the opposite direction of the normal, towards the BC face. 

• The glass-air boundary face AC is where the beam FS leaves the glass prism. The emerging ray is the ray FS that, following a series of refractions, exits the glass prism at face AC. 

• The emergent ray is often bent in the direction of the prism's base (BC), as depicted. 

• The angle of deviation D is the angle formed by the incident ray PE (when extended) and the emergent ray FS (when produced backwards to meet at a point G).

A Ray of Light Incident on a Prism 

• The angle of deviation is influenced by the prism's angle, angle of incidence, and material. 

• The condition for minimum deviation in prism can be  calculated by using following formula:

$\mu =\frac{\sin \frac{A+{{\delta }_{m}}}{2}}{\sin \frac{A}{2}}$ 

Where 

$\mu =$ refractive index, 

$A=$ angle of prism and 

${{\delta }_{m}}=$ minimum deviation.

Snell’s law of Prism and Its Formula

The law of refraction, also known as Snell's law, was discovered by Willebrord Snell in 1621. Snells’ law states that “The angle that the incident light beam makes with the prism's surface and the difference in the refractive indices of the two media determine how much the light is bent.” Snell's law describes the degree of refraction and the connection between an angle of incidence, an angle of refraction, and the refractive indices of a particular pair of media.

Formula:

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

where i denotes the angle of incidence and r the angle of refraction. The refractive index of the second medium with respect to the first is this constant value.

Angle of Prism

The prism angle formula is as follows:

$\mu =\frac{\sin \frac{A+{{\delta }_{m}}}{2}}{\sin \frac{A}{2}}$

Where $\mu =$ refractive index, $A=$ angle of prism and ${{\delta }_{m}}=$ minimum deviation.

Application of Prism

There are various applications for prisms. To fit particular purposes, they are produced in a wide variety of forms and shapes. In optical devices including microscopes, lenses, telescopes, and laser diodes, prisms are frequently used. Other examples include:

• Interferometry.

• Pattern recognition.

• Rangefinders.

• Laser instrumentation.

• Beam steering.

• Tunable lasers.

• Forestry.

• Stereo microscopes.

Conclusion

A polyhedron with a triangle base and three rectangular lateral surfaces is referred to as a prism. It serves as an optical tool for studying how white light behaves when it passes through it. The angles at which the light bends include the angles of incidence, reflection, refraction, and deviation. 

When the incident ray enters the prism, it bends towards the normal, and when it exits the prism, it bends away from the normal. With the increase in the angle of incidence, the angle of deviation decreases. It rises with an increase in the angle of incidence until it reaches the minimum value. Both the incidence angle and the emergence angle are almost equal. The angle of refraction will be smaller than the angle of incidence when the light moves from a more common to a more dense optical medium.