Revision: Optics (Ray and Wave Optics) >> Refraction and Dispersion of Light through a Prism Physics (Theory) ISC (Science) ISC Class 12 CISCE

A prism is a homogeneous, transparent medium bounded by two plane surfaces inclined to each other at an angle.

The angle between the direction of the incident ray (produced forward) and the emergent ray (produced backward) is called the angle of deviation.

When white light passes through a thin prism, the ratio of the angular dispersion between the violet and the red emergent rays and the deviation suffered by a mean ray (ray of yellow colour) is called the ‘dispersive power' of the material of the prism. It is denoted by ω.

The coloured arcs seen in the sky when sunlight is dispersed by raindrops are called rainbows.

When sunlight passes through the Earth's atmosphere, much of the light is absorbed by the fine dust particles and air molecules in the atmosphere, which give out the absorbed light in some other direction. This is 'scattering of light'.

The angle between the emergent rays of any two colours is called ‘angular dispersion’ between those colours.

θ = (n_V - n_R) A

ω = \[\frac{n_{V}-n_{R}}{n_{Y}-1}\]

Internationally Accepted: 

ω = \[\frac{n_{F}-n_{C}}{n_{D}-1}\]

n = \[\frac{\sin\frac{A+\delta_{m}}{2}}{\sin\frac{A}{2}}\]

Rayleigh proved that the intensity of scattered light is inversely proportional to the fourth power of the wavelength; provided the scatterer is smaller in size than the wavelength of light :

Scattering ∝ \[\frac {1}{λ^4}\]

According to this law, the short waves of violet light (λ = 4000) are scattered about ten times more than the longer waves of red light (λ = 7000). The other colours are scattered by intermediate amounts.

• Scattering of light by air molecules and fine dust particles explains many atmospheric optical phenomena.
• The sky appears blue because shorter-wavelength blue light scatters more strongly than red light in the atmosphere.
• If there were no atmosphere, the sky would appear black, as no scattering of sunlight would occur.
• Clouds appear white because water droplets and ice crystals are large and scatter all wavelengths nearly equally.
• The Sun appears reddish at sunrise and sunset because blue light scatters more strongly over a longer atmospheric path.
• Red light is used in danger signals because it suffers the least scattering and can be seen from long distances.
• Infra-red rays suffer very little scattering, so infra-red photography is possible in fog and mist.

• Rainbows are formed due to the dispersion of sunlight in raindrops.
• The primary rainbow is formed after one internal reflection in a raindrop and is brighter, with violet inside and red outside.
• The secondary rainbow is formed after two internal reflections and is fainter, with red inside and violet outside.
• The primary rainbow is seen at about 41°–43°, while the secondary rainbow is seen at about 51°–54° from the antisolar direction.
• Primary and secondary rainbows appear as concentric arcs with a common centre on the line joining the sun and the observer.

• The limiting angle of incidence is the angle at which a ray just emerges from the prism; for angles smaller than this, total internal reflection occurs at the second face.
  \[i_1=\sin^{-1}\left[\sqrt{(n^2-1)}\sin A-\cos A\right]\]
• For grazing incidence and grazing emergence, both angles of incidence are 90^∘, and the condition for emergence is
  A ≤ 2Ca​
  where C is the critical angle.
• Maximum deviation by a prism occurs when the angle of incidence at the first face is 90^∘ (grazing incidence).
  δ_max = δ₁ + δ₂ = (90° – C) + (i – r).

• The deviation produced by a prism depends on the angle of incidence, the angle of the prism, and the material of the prism.
• As the angle of incidence increases, the angle of deviation first decreases, becomes minimum, and then increases.
• For minimum deviation, the angle of incidence equals the angle of emergence (i = i′).
• In the condition of minimum deviation, the refracted ray inside the prism travels parallel to the base of the prism.
• For a thin prism, the deviation depends only on the refractive index of the material and the angle of the prism, and not on the angle of incidence.