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The Human Eye and Optical Phenomena - DISPERSION OF WHITE LIGHT BY A GL10.4 DISPERSION OF WHITE LIGHT BY A GL10.4 DISPERSION OF WHITE LIGHT BY A GL10.4 DISPERSION OF WHITE LIGHT BY A GL10.4 DISPERSION OF WHITE LIGHT BY A GL ASS PRISMASS PRISMASS PRISM

Grade 10CBSE

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

🔑Concepts

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Dispersion: The phenomenon of splitting of white light into its constituent seven colors when it passes through a transparent medium like a glass prism is called dispersion.

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Spectrum: The band of the colored components of a light beam is called its spectrum. The sequence of colors is VIBGYOR: Violet, Indigo, Blue, Green, Yellow, Orange, and Red.

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Cause of Dispersion: Different colors of light travel with the same speed in vacuum but different speeds in a refractive medium. Since refractive index n=cvn = \frac{c}{v}, the medium offers different refractive indices for different colors.

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Bending and Wavelength: Red light has the maximum wavelength and travels fastest in glass, so it deviates the least. Violet light has the minimum wavelength and travels slowest, so it deviates the most.

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Angle of Deviation (δ\delta): The angle between the direction of the incident ray and the emergent ray is known as the angle of deviation.

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Newton's Experiment: Sir Isaac Newton used two identical glass prisms, one in an upright position and the other in an inverted position. The first prism dispersed white light into a spectrum, and the second (inverted) prism recombined the spectrum back into white light.

📐Formulae

v=fλv = f \lambda

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

A+δ=i+eA + \delta = i + e

δ∝1λ\delta \propto \frac{1}{\lambda}

nv>nr  ⟹  δv>δrn_{v} > n_{r} \implies \delta_{v} > \delta_{r}

💡Examples

Problem 1:

A ray of white light passes through a glass prism. If the angle of incidence is 40∘40^{\circ}, the angle of the prism is 60∘60^{\circ}, and the angle of emergence is 45∘45^{\circ}, calculate the angle of deviation.

Solution:

Given: Angle of prism A=60∘A = 60^{\circ}, Angle of incidence i=40∘i = 40^{\circ}, Angle of emergence e=45∘e = 45^{\circ}. Using the prism relation: A+δ=i+eA + \delta = i + e δ=(i+e)−A\delta = (i + e) - A δ=(40∘+45∘)−60∘\delta = (40^{\circ} + 45^{\circ}) - 60^{\circ} δ=85∘−60∘=25∘\delta = 85^{\circ} - 60^{\circ} = 25^{\circ}

Explanation:

The angle of deviation is the sum of the angles of incidence and emergence minus the angle of the prism.

Problem 2:

Why does red light appear at the top and violet at the bottom of the spectrum formed by a prism?

Solution:

The refractive index of glass is higher for violet light (nvn_{v}) than for red light (nrn_{r}). Since deviation δ\delta is directly proportional to the refractive index (nn), we have: nv>nr  ⟹  δviolet>δredn_{v} > n_{r} \implies \delta_{violet} > \delta_{red}

Explanation:

Because red light bends the least, it stays at the top of the spectrum, whereas violet light bends the most and appears at the bottom.

Problem 3:

Calculate the refractive index of a medium if the speed of a specific color of light in that medium is 2×108 m/s2 \times 10^{8} \text{ m/s}. (Speed of light in vacuum c=3×108 m/sc = 3 \times 10^{8} \text{ m/s})

Solution:

Using the formula for refractive index: n=cvn = \frac{c}{v} n=3×1082×108n = \frac{3 \times 10^{8}}{2 \times 10^{8}} n=1.5n = 1.5

Explanation:

Refractive index is a dimensionless quantity representing the ratio of the speed of light in a vacuum to its speed in a given medium.