Single Choice

The graph between angle of deviation $$(\delta )$$ and angle of incidence (i) for a triangular prism is represented by:

A
B
Correct Answer
C
D

Solution

In the given figure,
$$ \theta_4=\sin^{-1}n\sin(\theta_3) $$
$$ A+\delta=\theta_1+\theta_4 $$
$$ A=\theta_2+\theta_3 $$
$$ \delta=\theta_1+\sin^{-1}n\sin(\theta_3)-A $$
$$ \delta=\theta_1+\sin^{-1}n\sin(A-\theta_2)-A $$

$$ \delta=\theta_1+\sin^{-1}n\sin(A-\sin^{-1}\dfrac{\sin(\theta_1)}{n})-A $$

Plotting this on the graph, we get a graph like (b).
But deducing that just by looking at the equation is difficult.
To deduce it, we can first conclude that the curve will be nonlinear and continuous.
Secondly, mimimum deviation occurs only at 1 value of angle incidence.
Hence answer is B

SIMILAR QUESTIONS

Optics

Light is incident from glass $$(\mu = 1.5)$$ to air. Sketch the variation of the angle of deviation $$\delta$$ with the angle of incident $$i$$ for $$0 < i < 90^o$$.

Optics

Light is incident from glass $$(\mu = 1.50)$$ to water $$(\mu = 1.33)$$. Find the range of the angle of deviation for which there are two angles of incidence.

Optics

There is a glass prism of refractive index $$\mu$$ and angle of prism is $$A$$. A ray of light enter the side $$AB$$ face of the prism at an angle of incident $$i$$. The value of angle of incident $$i$$ so, that no ray emerges from the face $$AC$$ of the prism is :

Optics

In a glass prism, spectrum is produced due to :

Optics

A ray of light travels from a medium of refractive index $$ \mu $$ to air. Its angle of incidence in the medium is $$\theta$$, measured from the normal to the boundary, and its angle of deviation is $$ \delta $$.$$ \delta $$ is plotted against $$\theta$$. Which of the following best represents the resulting curve?

Optics

The refractive index of a prism for a monochromatic wave is $$\sqrt { 2 }$$ & its refractive angle is $${ 60 }^{ o }$$ . For a minimum deviation, the angles of incidence will be:

Optics

For a prism, graph between angle of deviation($$\delta$$) and angle of incidence will be

Optics

What should be the angle between two plane mirrors, so that whatever be the angle of incidence, the incident ray and the reflected ray from the two mirrors be parallel to each other?

Optics

Following figure shows the multiple reflections of a light ray along a glass corridor where the walls are either parallel or perpendicular to one another. If the angle of incidence at point P is $${ 30 }^{ \circ }$$, what are the angles of reflection of the light ray at point Q, R, S and T respectively-

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