Problems in lenses and mirrors - Problem L2

We have seen rearview mirror used in vehicles.

This mirror is used to keep an eye on all the traffic behind you.

Convex mirror is used as a rear view mirror because they give an erect and virtual image of the distant objects.

And the image formed by a convex mirror virtual, erect and diminished.

And therefore it can form an image of a large area in a small mirror.

Now, we will study the problems related to mirrors and lenses.

Let’s understand the problems in lenses and mirrors.

Suppose, a biconvex lens of focal length is placed in front of a plane mirror.

The distance between the lens and the mirror is .

Now, small object is kept at a distance of from the lens.

Let’s see the formation of the image with lens and mirror.

The focal length of the biconvex lens is .

A small object is placed at a distance of from the lens that is at a distance of .

Therefore, the image should form at from the lens at .

But since the ray strikes the plane before reaching , the image acts as the virtual object for reflection on the plane mirror.

And that is kept at a distance of from it.

It will produce image but as the ray encounters the lens, it gets refracted.

And the final image is formed at .

For the last refraction from the biconvex lens, the object distance is shown as,

Now, we use lens formula to find the image distance.

A lens formula relates the object distance , and image distance to the focal length of the lens.

Substitute all the values in the lens formula as

Now, solve this equation and find the image distance.

Therefore, a real image is formed at a distance of from the plane mirror.

Revision

A lens formula relates the object distance , and image distance to the focal length of the lens.

The End