krit.club logo

The Human Eye and the Colourful World - Refraction of light through a prism

Grade 10CBSE

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

🔑Concepts

•

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 (denoted by AA).

•

Refraction through a prism: When a ray of light enters a prism, it bends towards the normal at the first surface (air to glass) and away from the normal at the second surface (glass to air).

•

The Angle of Deviation (DD or δ\delta) is the angle formed between the incident ray produced forward and the emergent ray produced backward.

•

Dispersion: The phenomenon of splitting of white light into its constituent seven colors (VIBGYOR) when passed through a glass prism. This happens because different colors of light travel at different speeds in a glass prism, meaning the refractive index nn is different for each color.

•

In the visible spectrum, Red light has the longest wavelength (λred\lambda_{red}) and deviates the least, while Violet light has the shortest wavelength (λviolet\lambda_{violet}) and deviates the most.

•

Isaac Newton's Experiment: By using two identical prisms, one in an upright position and the other in an inverted position, Newton showed that the dispersed spectrum could be recombined to form white light again.

•

Rainbow Formation: A natural spectrum appearing in the sky after rain, caused by the dispersion of sunlight by tiny water droplets. The process involves three steps: Refraction, internal reflection, and then dispersion/refraction again.

📐Formulae

i+e=A+Di + e = A + D

n=sin⁡(A+Dm2)sin⁡(A2)n = \frac{\sin(\frac{A + D_m}{2})}{\sin(\frac{A}{2})}

v=fλv = f \lambda

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

💡Examples

Problem 1:

A ray of light is incident on one face of a glass prism with an angle of 60∘60^\circ. If the angle of incidence ii is 45∘45^\circ and the angle of emergence ee is 40∘40^\circ, calculate the angle of deviation DD.

Solution:

Given: Angle of Prism A=60∘A = 60^\circ, Angle of incidence i=45∘i = 45^\circ, Angle of emergence e=40∘e = 40^\circ. Using the formula i+e=A+Di + e = A + D, we substitute the values: 45∘+40∘=60∘+D45^\circ + 40^\circ = 60^\circ + D. Therefore, 85∘=60∘+D  ⟹  D=85∘−60∘=25∘85^\circ = 60^\circ + D \implies D = 85^\circ - 60^\circ = 25^\circ.

Explanation:

The angle of deviation is the sum of the incident and emergent angles minus the angle of the prism.

Problem 2:

Which color of white light deviates the most when passing through a prism, and why?

Solution:

Violet light deviates the most. This is because violet light has the shortest wavelength (λ\lambda) in the visible spectrum. According to the relationship between refractive index and wavelength, the refractive index nn is higher for shorter wavelengths. Thus, the glass prism offers more resistance and bending to violet light than to red light.

Explanation:

The degree of bending depends on the change in speed; since violet light slows down the most in glass, it undergoes the maximum refraction.