Question

Draw a ray diagram to show the refraction of a monochromatic ray through a prism when it suffers minimum deviation.

Answer 1

Hint: As we all know when a light deviates with a minimum amount after refraction through the prism, angle of incidence (i) and the angle of emergence (e) are equal.

Complete step by step answer:

The above diagram shows the path of light traced when it passes through a prism such that the angle of deviation of light is minimum.
We know that deviation angle, $\delta$is given by
$\delta =i+e-A$
Where $i$ is the angle of incidence
$e$ is the emergent angle
$A$ is the angle of prism.
Thus, the angle of deviation depends upon the angle of incidence. A plot between angle of deviation and angle of incidence is shown below from where it is clear that corresponding to$i=e$, $\delta$is minimum and for all other values of $i$, there are two values of $\delta$.
So, at minimum deviation$i-e$.
$\delta =\delta m,\text{ i}=e$

When a light deviates with a minimum amount, the angle of incidence and the angle of emergence are equal.
Also, the light inside the prism passes parallel to the base of prism BC.

Note:
If a ray enters the prism from air with a refractive index $$n_1=1$$, the direction of the ray after it passes through the prism will depend only on its apex angle Q and the refractive index n of the glass from which prism is made. Passage of a ray through an optical prism is depicted in the picture above.