Name: Ray Diagram: Lenses
Uploaded: 2019-07-19
Duration: 6 min 35 s
Description: In this video, let us discuss how ray diagrams for lenses can be used to determine the size and location of a refracted image. Get in to know more!

Question

Define Snell's Law. Using a neat labelled diagram derive an expression for the refractive index of the material of an equilateral prism.

Accepted Answer

The ratio of the sine of the angle of incidence to the sine of angle of refraction is constant.
$\frac{\sin i}{\sin r} = μ (constant)$
Consider $A B C$ be the glass prism. Its angle of prism is $A$ . The refractive index of the material of the prism is $μ$ . $P Q$ be the incident ray on surface $A B$ and $R S$ be the emergent ray from the surface $A C$ . Such that, incident ray and emergent ray makes angle of incidence $i$ and angle of emergence $e$ with normals $M$ and $N$ respectively.

Angle of incidence $= i$ , Angle of emergence $= e$

Angle of refraction at $Q$ is $= r_{1}$ , Angle of refraction at $R$ is $= r_{2}$

From the $∆ Q R T$

$r_{1} + r_{2} + ∠ T = 180 °$ ......( $1$ )

From the quadrilateral $A Q T R$

$∠ A + ∠ T = 180 °$

$∠ T = 180 ° - A$ .....( $2$ )

From equations (1) and (2)

$r_{1} + r_{2} + 180 ° - A = 180 °$

$\Rightarrow r_{1} + r_{2} = A$ ....( $3$ )

From the $∆ Q O R$

$i - r_{1} + e - r_{2} + 180 ° - D = 180 °$

$i + e - A = D (∵ r_{1} + r_{2} = A)$

$i + e = A + D$ .....( $4$ )

For minimum angle of deviation

$∴ i = e, r_{1} = r_{2} = r$

Substituting values in equation (3) and (4) we get

$r = \frac{A}{2}$

$i + e = A + D \Rightarrow i = \frac{A + D}{2}$

According to snell's law $μ = \frac{\sin i}{\sin r}$

$\Rightarrow μ = \frac{Sin (\frac{A + D}{2})}{Sin (\frac{A}{2})}$

Define Snell's Law. Using a neat labelled diagram derive an expression for the refractive index of the material of an equilateral prism.

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