Question

Assertion: We cannot produce a real image by plane or convex mirrors under any circumstances.
Reason: If image distance of a real object in front of a convex mirror is taken as negative, the focal length of a convex mirror is taken as positive.
(A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
(B) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion
(C) Assertion is correct but Reason is incorrect
(D) Assertion is incorrect but Reason is correct

Answer 1

When reflected rays meet in front of the mirror, the image formed is known as real image, whereas when the reflected rays appear to meet behind the mirror, the image formed is known as a virtual image.

Complete step by step solution:
A mirror is any reflective surface from which most of the light rays get reflected. The light rays falling on the surface of the mirror are known as incident rays. The point at which the ray falls, is known as the point of incidence. And the light rays which get reflected from the mirror are known as reflected rays.
The point at which the incident rays meet or appear to meet is known as the object. And the point at which the reflected rays meet or appear to is known as the image.
Now mirrors are of two types – Plane mirror and Spherical mirror. Their names signify their shape. That is, the plane mirror is in the shape of a plane surface whereas the spherical mirrors are in the shape of a mirror. Spherical mirrors are also of two types – Convex mirror and Concave mirror.
When the inward surface of the sphere is made into the reflective surface, also known as a concave surface, that mirror is known as a concave mirror. But when the outer surface of the sphere is silvered, also known as the convex surface, that mirror is known as the convex mirror.
Now, all the measurements related to mirrors are done by relating the mirror to a Cartesian system. Which means that the mirror is kept at the Y-axis, with its pole at the origin. And the silvered surface always faces the negative x-axis, and the surface which exists behind the mirror faces the positive x-axis.
So any measurement taken in front of the mirror is taken in negative and any measurement taken behind the mirror is taken in negative.
Now plane mirrors and convex mirrors are known to produce virtual images. But that’s not completely true, plane mirrors and convex mirrors produce virtual images of real objects and real images of virtual objects. Which means that if the object is present in front of the mirror, the image would be formed behind the mirror whereas if the object is present behind the mirror, the image is formed in front of the mirror. Now how does someone place an object behind the mirror? It is depicted by the given diagram,


In the above diagrams, we can see that at point O, the incident rays do not actually meet and thus create a virtual object. And at point I, we can see that the reflected rays actually meet, thus forming a real image.
So we conclude that plane mirrors and convex mirrors can form a real image and thus Assertion is incorrect.
Now, focus of a mirror is defined as the point at which the reflected rays of the rays coming from infinity meet or appear to meet. And the distance of focus from the pole of the mirror is known as its focal length. It's usually equal to half of the radius of curvature of the mirror. Now, since in a convex mirror, both focus and center of curvature lie behind the mirror, the values of focal length and radius of curvature are taken in positive. This concludes the fact that the Reason is correct.

Therefore, option D is the correct answer.

Note: Concave mirrors are usually used for the formation of real images, since we do not need a virtual object in the case of a concave mirror to produce a real image. The apparatus at which we obtain and observe the real image is known as a screen. And this is the same technology which is used in a camera.