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Deviation produced by thin prism

Deviation produced by thin prism :- A prism with small angle of prism(refracting angle or apex angle) A ≤ 10°, is called a thin prism. Thin prisms introduce small angular beam deviations(δ) and this deviation is approximately independent of the angle of incidence.

Considering the figure of previous article Refraction of light through a prism, applying Snell’s law at interface AB,

$\displaystyle \frac{\sin {{i}_{1}}}{\sin {{r}_{1}}}=\mu$ …..(1)

For thin prism, angles i₁ and r₁ are very small, so

$\displaystyle \sin {{i}_{1}}\approx {{i}_{1}}\text{ and }\sin {{r}_{1}}\approx {{r}_{1}}$

hence from equation(1), we get

$\displaystyle {{i}_{1}}=\mu {{r}_{1}}$ …..(2)

Similarly, applying Snell’s law at interface AC,

$\displaystyle \frac{\sin {{r}_{2}}}{\sin {{i}_{2}}}=\frac{1}{\mu }$ …..(3)

As angle are small,

$\displaystyle \sin {{r}_{2}}\approx {{r}_{2}}\text{ and }\sin {{i}_{2}}\approx {{i}_{2}}$

So from equation (3),

$\displaystyle {{i}_{2}}=\mu {{r}_{2}}$ …..(4)

Now deviation produced by prism is given by,

δ = i₁ + i₂ – A

⇒ δ = μr₁ + μr₂ – A

⇒ δ = μ(r₁ + r₂) – A

As r₁ + r₂ = A

⇒ δ = μA – A

Hence

Deviation produced by thin prism(δ) = (μ– 1)A

Illustration 1.

Calculate the deviation produced by a prism of angle 6°, given refractive index of the prism is 1.644.

Solution:-

Using

δ = (μ– 1)A = (1.644 – 1) × 6 = 3.864°

Deviation produced by thin prism

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