Question

If the incident ray passes through focus, then the reflected ray is_________ to the principal axis in the concave mirror.
(A) ${45^ \circ }$ inclined
(B) Perpendicular
(C) Parallel
(D) None of these

Answer 1

To solve this question, we need to use the mirror equation. We have to substitute the object distance and the focal length with the proper sign convention in the mirror equation to get the image distance. From the value of the image distance, we can get the final answer.

Formula used: The formula used to solve this question is given by
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ , here $f$ is the focal length of a mirror, $u$ is the object distance, and $v$ is the image distance.

Complete step-by-step solution
Let $f$ be the focal length of the given concave mirror.
We know from the mirror equation that the image distance, the object distance, and the focal length of a mirror are related by the mirror equation, which is given by
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
Now, according to the question, the incident ray passes through the focus of the concave mirror. So we can assume our object to be kept at the focus of the given concave mirror. This means that the object distance is equal to the focal length of the mirror. According to the Cartesian sign convention, the focal length and the object distance for a concave mirror are taken as negative. So we substitute $u = - f$ and $f = - f$ in the above equation, we get
$\dfrac{1}{v} + \dfrac{1}{{ - f}} = \dfrac{1}{{ - f}}$
$\Rightarrow \dfrac{1}{v} = 0$
Taking the reciprocals on both the sides, we finally get
$v = \infty$
So the image is formed at the infinity. This means that the reflected rays will meet at an infinite distance from the mirror. This implies that the reflected rays will be parallel to the principal axis of the concave mirror.
Hence, the correct answer is option C.

Note
The above statement is true not only for a concave mirror, but for every kind of optical instrument. Be it a convex mirror, a concave or a convex lens. The incident ray which passes through the focus, or appears to be passing through the focus, becomes parallel to the principal axis after getting reflected or refracted.