Question
A plot between the angle of deviation (δ) and angle of incidence (i) for triangular prism is shown below. Explain any given value of ‘δ’ corresponds to two values of angle of incidence? State the significance of point P on the graph. Use this information to derive an expression for refractive index of the material of the prism.
Solution
Generally, any given value of angle of minimum deviation , corresponds to two values i and e, except for i = e. This, in fact, is expected from the symmetry of i and e as,
δ = i + e – A,
i.e., δ remains the same even if i and e are interchanged.
Fig.(a)
In the fig. above, point P is the point of minimum deviation. This is related to the fact that the path of the ray as shown in fig (b) can be traced back, resulting in the same angle of deviation.
Fig. (b)
At the minimum deviation Dm, the refracted ray inside the prism becomes parallel to the base.
For, δ = Dm;
we have, i = e and,
In the same way,
∴ The refractive index of the prism is
δ = i + e – A,
i.e., δ remains the same even if i and e are interchanged.
Fig.(a)
In the fig. above, point P is the point of minimum deviation. This is related to the fact that the path of the ray as shown in fig (b) can be traced back, resulting in the same angle of deviation.
Fig. (b)
At the minimum deviation Dm, the refracted ray inside the prism becomes parallel to the base.
For, δ = Dm;
we have, i = e and,
In the same way,
∴ The refractive index of the prism is
