1. What a prism does to light
A prism is a transparent optical block with flat, polished surfaces arranged at angles. When light enters and leaves a prism, it bends twice — once at the first surface and again at the second. Because of these two refractions, the outgoing ray is shifted from its original direction.
This shift is called deviation. A prism doesn't just bend light; it can also separate white light into different colours, a phenomenon called dispersion.
2. Basic structure of a triangular prism
The most common prism has two refracting surfaces and one base. Some simple terms I use in prism diagrams:
- Apex (A): The angle between the two refracting surfaces.
- Refracting faces: The two surfaces where refraction happens.
- Base: The third surface.
- Incident ray: The ray entering the first surface.
- Emergent ray: The ray leaving the second surface.
- Angle of deviation (δ): The angle between the original incident direction and the emergent direction.
3. How a prism bends light
When a ray enters the first surface, it bends according to Snell’s law. Inside the prism, the ray travels at an angle to the base. When it reaches the second surface, it bends again.
The overall bending (deviation) depends on:
- the prism's material (its refractive index),
- the angle at which light enters,
- the prism’s apex angle.
3.1. Deviation explained simply
The total deviation is the difference between the direction of the incident ray and the direction of the emergent ray. If the prism is made of a denser material, the bending is stronger, so deviation is larger.
4. Prism formula for minimum deviation
At one special angle, the emergent ray comes out symmetrical to the incident ray. At this position, the deviation is the least. This is called the angle of minimum deviation \(\delta_m\).
At minimum deviation, the refractive index of the prism material is given by:
\( n = \dfrac{\sin\left(\dfrac{A + \delta_m}{2}\right)}{\sin\left(\dfrac{A}{2}\right)} \)
Here:
- \(A\) is the apex angle,
- \(\delta_m\) is the minimum deviation.
I use this formula to calculate the refractive index of prism materials in experiments.
5. Dispersion of light by a prism
White light is made of many wavelengths. Different wavelengths have slightly different refractive indices in glass. Because of this, each colour bends by a different amount inside a prism.
5.1. Order of colours
Shorter wavelengths (like violet) bend more, and longer wavelengths (like red) bend less. This creates a spectrum in the order:
Violet → Indigo → Blue → Green → Yellow → Orange → Red
Violet deviates the most, red the least.
6. Why different colours bend differently
The refractive index of a material depends slightly on wavelength. This is called dispersion. Prism materials generally have higher refractive index for violet light and lower for red light. Since bending depends on refractive index, each colour emerges in a different direction.
7. Deviation vs dispersion
I like to think of these two effects separately:
- Deviation → how much the entire ray is shifted.
- Dispersion → how much the colours spread apart.
A prism always causes deviation. It causes dispersion only when light contains more than one wavelength (like white light).
8. A simple example
If white light enters a glass prism of apex angle \(60^\circ\), the emerging beam splits into a spectrum. If the angle of minimum deviation is observed to be \(38^\circ\), then:
\( n = \dfrac{\sin\left(\dfrac{60 + 38}{2}\right)}{\sin\left(\dfrac{60}{2}\right)} = \dfrac{\sin 49^\circ}{\sin 30^\circ} = \dfrac{\sin 49^\circ}{0.5} \)
This gives the refractive index of the prism material. Using the same setup, I can also observe how far the colours spread out.
9. Where prisms appear in daily life
Prisms are used in various setups and devices:
- Periscopes and binoculars (for internal reflections).
- Prism-based spectrometers.
- Camera viewfinders.
- Rainbow formation (nature’s own prism effect).
Once I understood prism refraction and dispersion, many colourful optical effects became easier to explain.