What Is a Prism? Definition, Properties, and Examples

A prism is a transparent optical element with flat, polished surfaces that refract light. Frequently, prisms are used to disperse white light into its constituent spectrum or to change the direction and orientation of beams in optical systems. Prisms are typically made from glass, acrylic, or other transparent materials and are widely studied in optics due to their refractive and dispersive properties.

Definition and Structure of Prism

A prism is a wedge-shaped object bounded by two non-parallel plane faces known as the refracting faces. The angle between these faces is called the angle of prism or the refracting angle. The base of the prism connects these two faces, giving it a typical triangular cross-section.

Materials such as glass or plastic are commonly used to manufacture prisms as they provide transparency for visible light. Both sides and bases of prisms are polished to ensure minimal loss of light due to scattering or absorption.

Working Principle of a Prism

When a ray of light enters a prism, it undergoes refraction at the first interface. As it passes through the prism and reaches the second interface, it is refracted again. This double refraction causes both deviation and dispersion of light depending on the wavelength and angle of incidence.

The refractive index of the prism material and the angle of the prism determine the extent of deviation and dispersion. The relationship between these quantities is essential for understanding the functioning of optical instruments.

For detailed ray tracing and the angle of deviation with respect to a prism, refer to Path of Ray of Light Through Prism.

Refraction and Deviation in a Prism

When light enters from air (rarer medium) to glass (denser medium), it bends towards the normal. Upon leaving the prism, the light moves from denser to rarer medium and bends away from the normal. The emergent ray is thus deviated from its original path.

Let $A$ be the angle of prism and $i$ and $e$ represent the angle of incidence and emergence. $r_1$ and $r_2$ are the angles of refraction at the two faces respectively. The following relationships are used for calculations:

The sum of the angles of refraction inside the prism is given by:

$r_1 + r_2 = A$

The angle of deviation $\delta$ is:

$\delta = (i + e) - A$

At minimum deviation, $i = e$ and $r_1 = r_2 = r$, so:

$2r = A \implies r = \dfrac{A}{2}$

The refractive index $\mu$ of the prism can be found using:

$\mu = \dfrac{\sin\left(\dfrac{A + D_{min}}{2}\right)}{\sin\left(\dfrac{A}{2}\right)}$

For more on deviation, see Angle of Deviation in Prism.

Dispersion of Light by a Prism

A principal use of a prism is its ability to separate white light into its constituent colours, a phenomenon known as dispersion. The refractive index varies with wavelength; shorter wavelengths like blue light are refracted more than longer wavelengths like red light.

This property is exploited in spectrometers and refractometers to analyze light into its spectrum or measure refractive indices accurately.

Types of Prisms

Prisms exist in various forms and are used for different optical purposes. The classification is based on application and the optical property being utilized.

• Dispersive prisms for spectrum formation
• Reflective prisms for image orientation
• Beam-splitting prisms to divide light beams
• Polarizing prisms for producing plane-polarized light
• Deflecting prisms for steering light direction

For the use of prisms in splitting and polarization, refer to Sign Convention in Optics.

Dispersive Prism

Dispersive prisms, such as the standard triangular prism, are designed to separate incident white light into its spectral colours. The refractive index being wavelength-dependent causes each colour to deviate by a different amount. Blue light bends more than red light due to its higher refractive index in the prism material.

Reflective Prisms

Reflective prisms are mainly utilized to alter the path, orientation, or parity of images in optical instruments. Total internal reflection is often achieved within such prisms to maximize reflectivity. Porro prisms are widely used in binoculars to invert and revert images.

Beam-Splitting and Polarizing Prisms

Beam-splitting prisms, such as dichroic prisms, separate an incident light beam into two or more beams based on wavelength. Polarizing prisms, for example, Nicol prism, are constructed from birefringent crystals and separate the incoming beam into ordinary and extraordinary rays.

Deflecting Prisms

Deflecting prisms are designed to change the propagation direction of light by a specified angle. They are used in beam steering applications such as Risley prism pairs, where the rotation of the prisms enables variable beam deflection within a certain cone angle.

Ray Tracing Through a Prism

The path of a light ray through a prism involves two refractions: entry and exit. At each refracting face, the direction of light bends according to Snell’s Law. The net result is that the emergent ray is deviated from the path it would have taken if the prism was absent.

A comparison between displacement in a glass slab and a prism demonstrates that, while glass slabs cause parallel displacement, prisms result in deviation and non-parallel emergent rays.

Refer to Lateral Displacement of Light for a detailed evaluation of light displacement in optical elements.

Minimum Deviation and Refractive Index

At minimum deviation, the emergent ray is symmetric with respect to the prism base and both angles of incidence and emergence are equal. This condition simplifies calculations of the prism’s refractive index and is applied in many experimental measurements for accuracy.

Applications of Prisms

Prisms are key components in spectrometers for spectral analysis, in binoculars for image correction, in cameras for viewfinder systems, and in various instruments for beam deviation, splitting, and polarity effects.

For advanced applications and ray diagrams, see Refraction of Light Through Prism.

In rotational systems like the conical pendulum, optical path manipulation by prisms forms the basis for controlling the direction and movement of light beams. Relevant principles are discussed in Conical Pendulum.