# Focal Length of Convex Mirror Experiment

Experiment: Find the focal length of a convex mirror using a convex lens.

A convex mirror always forms virtual image of a real object and hence the value of v (i.e. the position of the image) cannot be obtained directly. Therefore, convex lens is used to enable us to form a real image due to the combination.

Let an object O be placed between f and 2f of a convex lens L and its image be formed at I, which you locate by removing parallax between the image pin and the image of O.

Now keeping the position of O and L fixed, place the convex mirror between L and I at such a position so that the image of O is formed just above it. This happens when the rays retrace their path, i.e. when the rays falls on the mirror normally. This means that MI is the radius of curvature of the mirror.

Since, R = 2f

f = MI/2

Material Required

Convex mirror, convex lens (having focal length greater than that of the mirror but not greater than twice of that of the mirror), optical bench with four uprights, knitting needle, metre-rod, spirit level

### How To Set Up

1. Level the optical bench with the help of spirit level and leveling screws.

2. Mount the lens L in the middle of the bench and one pin on either side of it. Adjust the centre of the lens and tips of the pins in the same horizontal line.

3. Replace the pin I with mirror M. Check by moving M close to L that the combination of M and L behaves as a concave mirror and you receive an inverted image of O. In case inverted image is not obtained and combination still behaves as a convex mirror, then replace the lens with another convex lens of shorter focal length. ### How To Perform Experiment

1. Find the approximate focal length f1 of the convex lens.

2. Find the index-correction between the mirror M and the image needle I.

3. Place the object needle O at a distance greater than f1 and remove parallax between the tip of O and its real inverted image by lens-mirror combination, by adjusting the position of mirror M.

4. Fix the positions of O and L and M and note their positions.

5. Remove the mirror from its upright and mount the image needle I in its place. Without disturbing O and L remove parallax between the inverted image of O and the tip of the image needle I. Note the position of I.

6. The distance MI is observed radius of curvature of the convex mirror.

7. Repeat the experiment 4 to 5 times by changing distance between object needle and convex lens.

8. Find mean R and then f = R/2