Question 86: Ray Optics

Question

A thin prism with angle $5^{\circ}$ of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is $\_\_\_\_$ .

Accepted Answer

When two thin prisms are combined to produce dispersion without deviation, they are arranged such that their refracting angles are inverted relative to each other. The net deviation produced by the combination is zero.
$\delta_{	ext {net }}=\delta_1-\delta_2=0$
$$\Rightarrow $$ $$ \delta_1=\delta_2 $$
The deviation $(\delta)$ produced by a thin prism is given by the formula :
$$ \delta=(\mu-1) \mathrm{A} $$
where :
$\mu$ is the refractive index of the material.
A is the angle of the prism.
Since the deviations must be equal and opposite :
$$ \left(\mu_1-1ight) \mathrm{A}_1=\left(\mu_2-1ight) \mathrm{A}_2 $$
The angle of prism for first prism is $\mathrm{A}_1=5^{\circ}$ and its refractive index is $\mu_1=1.72$
The refractive index of the second prism is $\mu_2=1.9$
$$ (1.72-1) 	imes 5^{\circ}=(1.9-1) 	imes \mathrm{A}_2 $$
$$\Rightarrow $$ $$ 3.6=0.9 	imes \mathrm{A}_2 \Rightarrow \mathrm{~A}_2=\frac{3.6}{0.9}=4^{\circ} $$
Therefore, the angle of the second prism is $4^{\circ}$. Hence, the correct option is (B).

Answer

$5^{\circ}$

Answer

$4^{\circ}$

Answer

$4.5^{\circ}$

Answer

$6^{\circ}$

Ray Optics

A thin prism with angle 5^{\circ} of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is \_\_\_\_ .

Choose the correct answer: