Question

The deviation produced by an equilateral prism, when a ray of light is incident on it, does not depend on:
(A) angle of incidence
(B) color of light
(C) material of prism
(D) size of prism

Answer 1

We will first see the formula for the angle of deviation for an equilateral triangular prism and check its dependence on various parameters. The angle of deviation for an equilateral prism is given as the sum of angle of incidence and angle of reflection minus the prism angle. We will use this to answer our problem.

Complete answer:
Let us first assign some important terms that we are going to use in our problem.
Let the angle of incidence of the prism be equal to ‘i’ and let the angle of reflection at the second surface be equal to ‘r’.
Also, let the angle of deviation be $\delta$.
Then, this angle of deviation can be written as:
$\Rightarrow \delta =i+r-{{60}^{0}}$
Where, ${{60}^{0}}$ is the angle of prism of an equilateral triangle.
Also, the incident angle and the reflected angle are related to each other on the basis of Snell’s law. Mathematically, this can be written as:
$\Rightarrow \mu =\dfrac{\sin i}{\sin r}$
It can also be written as:
$\Rightarrow \mu =\dfrac{{{\lambda }_{\text{white light}}}}{{{\lambda }_{\text{colored light}}}}$
Where, $\mu$ is the refractive index of the material and it depends on the nature of material.
We can see that the expression of angle of deviation clearly depends upon the angle of incidence, angle of refraction and prism angle. Since, the angle of reflection depends on the refractive index, it means that the angle of deviation depends on the nature of material also.
Also, the color of light depends on the refractive index. So, different color of light has suffered different refractive indices, thus the angle of deviation depends on the color of light too.
Hence, from our above observation, the angle of deviation doesn’t depend on the size of the prism.

So, the correct answer is “Option D”.

Note: According to the formula for angle of deviation, we saw it only depending on a few factors. But, we should always check the dependence of these parameters on various different factors. Only by doing this, we can get an absolute dependence of any term on different factors.