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The Human Eye and the Colourful World - Dispersion of light

Grade 10CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A glass prism is a transparent object with two triangular bases and three rectangular lateral surfaces. The angle between its two lateral faces is called the Angle of the Prism (AA).

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When a ray of light passes through a prism, it bends towards the base of the prism. The angle between the incident ray and the emergent ray is known as the Angle of Deviation (δ\delta).

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Dispersion is the phenomenon of splitting of white light into its seven constituent colours (VIBGYORVIBGYOR) when it passes through a glass prism.

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The band of the colored components of a light beam is called its Spectrum. The order of colours is Violet, Indigo, Blue, Green, Yellow, Orange, and Red (VIBGYORVIBGYOR).

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The cause of dispersion is that different colours of light bend through different angles with respect to the incident beam as they pass through a prism. Red light bends the least, while violet light bends the most because the refractive index of glass is different for different wavelengths.

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Isaac Newton used two identical prisms, one in an upright position and the other in an inverted position, to show that the colours of the spectrum can be recombined to form white light.

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A Rainbow is a natural spectrum appearing in the sky after rain. it is caused by the dispersion of sunlight by tiny water droplets, which act like small prisms. The processes involved are refraction, dispersion, and internal reflection.

📐Formulae

∠A+∠δ=∠i+∠e\angle A + \angle \delta = \angle i + \angle e

n=cvn = \frac{c}{v}

Refractive Index (n)∝1λ\text{Refractive Index } (n) \propto \frac{1}{\lambda}

c=3×108 m/sc = 3 \times 10^8 \text{ m/s}

💡Examples

Problem 1:

A ray of light is incident on one face of a glass prism with an angle of incidence i=48∘i = 48^\circ. If the angle of the prism is A=60∘A = 60^\circ and the angle of emergence is e=44∘e = 44^\circ, calculate the angle of deviation δ\delta.

Solution:

Given: i=48∘i = 48^\circ, A=60∘A = 60^\circ, e=44∘e = 44^\circ. Using the prism formula: A+δ=i+eA + \delta = i + e. Substituting the values: 60∘+δ=48∘+44∘  ⟹  60∘+δ=92∘  ⟹  δ=92∘−60∘=32∘60^\circ + \delta = 48^\circ + 44^\circ \implies 60^\circ + \delta = 92^\circ \implies \delta = 92^\circ - 60^\circ = 32^\circ.

Explanation:

The sum of the angle of the prism and the angle of deviation is always equal to the sum of the angle of incidence and the angle of emergence.

Problem 2:

Which colour of white light deviates the most when passing through a prism, and why? Refer to the refractive index nn and velocity vv.

Solution:

Violet light deviates the most. This is because violet light has the shortest wavelength (λviolet<λred\lambda_{violet} < \lambda_{red}) in the visible spectrum. Since n∝1λn \propto \frac{1}{\lambda}, the refractive index of glass is highest for violet light. Using v=cnv = \frac{c}{n}, violet light travels at the slowest speed in the medium, causing the maximum bending.

Explanation:

The degree of bending depends on the change in speed. Since violet light slows down the most compared to its speed in vacuum, it undergoes the maximum deviation δ\delta.

Dispersion of light - Revision Notes & Key Formulas | CBSE Class 10 Science