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## How to find the focal length of convex mirror using convex lens?

How to find the focal length of convex mirror using convex lens?

We cannot use an optical method to determine the focal length of a convex mirror without using a convex (converging) lens since a convex mirror does not form a real image of an object in front of it or even parallel rays coming from infinity.

Therefore we have to use a convex mirror to determine the focal length of the convex mirror by an indirect method.

### STEP 1 DETERMINE THE ROUGH FOCAL LENGTH OF THE CONVEX LENS

First of all we take a convex lens and determine  its rough focal length by forming a real image of a distant object on a screen. The distance between the convex lens and the screen gives the rough focal length, since when the object is at infinity, the image formed by the convex lens is at its focus. This method is called the distant object method to estimate the focal length of a convex lens. The focal length of a concave mirror may also be estimated using this method.

Now, as we know the approximate focal length of the convex lens, keep an object- an optical pin or a lit candle in front of the convex lens at a distance around 2 times the rough focal length determined and place a screen on the other side so as to form a real image of the object on it. This adjustment is done so as to make the distances involved quite manageable.

When you get a clear and sharp image on the screen, mark the positions of the convex lens and the screen on the table.

Place the convex mirror in between the screen and the lens without disturbing the position of the candle and the lens.

Place the screen close to the candle. Carefully adjust the position of the convex mirror alone so that you get a sharp image on the screen which is now kept  at the position of and along with the candle. Mark the position of the convex mirror now.

The distance between the position of the convex mirror and the old position of the screen gives the radius of curvature of the convex mirror. (Since r = 2f; we can determine the focal length by dividing the distance with 2)

### Why the distance is r (2f)?

We know that when a ray of light is incident normally on the surface of a mirror, it retraces its path.

We also know that a line drawn from the centre of curvature of the mirror to the surface of a mirror is normal to the surface.

Therefore, when we are getting the image at the same position as the candle, it is formed by retracing of the rays, which means that the old position of the screen is at the position of the centre of curvature of the convex lens.

## Focal length of convex mirror using convex lens

It is given that the image formed by the convex mirror should be at radius of curvature . Why it should?

I guess that the question is based on the experiment to determine the focal length of a convex mirror using convex lens.

Initially a convex lens is used to obtain a real image of a candle. (or pin if you are doing the experiment using the optical bench) Then a convex mirror is kept in such a way that the image is obtained on the same position as the object. This happens when the rays are incident normal to the mirror. The rays of light incident normal to the mirror are directed towards the centre of curvature. Since the image was formed by the rays which are now reflected normally, the distance between the convex mirror and the original position of image gives the radius of curvature.

See the diagram for illustration.

## Broken spherical mirror and change in focal length

If a spherical mirror broken is there  change in focal length, radius of curvature, image distance,mirror height.

Answer. No change. As long as there is no change in the radius of curvature, there is no change in focal length. Mirror forms image based on geometry only as the course of rays are in the same medium.

## Graphene bubbles can help make auto focus lenses

A group of UK Physicists claim that they have developed graphene bubbles which can change its curvature and hence its focal length and power by applying small voltages. If developed, this can be used in mobile cameras and other such devices. This would better imitate the functioning of Human Eye too.

More details available at http://physicsworld.com/cws/article/news/47250

## A Numerical from Combination of thin lenses in contact

Two thin lenses of focal lengths f1=20cm and f2=60cm are placed in contact. find the focal length f3 of the combined lenses. find also the focal length f of a third lens placed in contact with these two that would result in overall focal length f11=-40cm. (Asked Young)

## A numerical Problem from optics

When an object is kept at a distance of 60cm from a concave mirror, the magnification is 1/2. Where should the object be placed to get magnification of 1/3??

Ans:

In the first part, u=-60, m=(-)1/2 implies v=-30 cm (Since the image must be real as concave lens form virtual image of bigger size only)

Substituting in eqn

or

we get f = –20 cm

In II case

m=-1/3

v=u/3

f=-20cm

substituting in

we get u=4f=4 x (-20)=-80 cm

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