# To measure the focal length of a concave mirror

To measure the focal length of a concave mirror

We have already seen (Fig. 22.7) that when an object is placed at the centre of curvature of a concave mirror a real image is formed at the same place as the object. This fact is used in the following two methods for finding the focal length of a concave mirror. Method (1). Using an illuminated object at C. The object used in this experiment consists of a hole cut in a white screen made of sheet metal and illuminated from behind by a pearl electric lamp. Sharpness of focusing will be greatly assisted if a
thin cross-wire is placed across the hole (Fig. 22.16).

A concave mirror, mounted in a holder, is moved to and fro in front of the screen until a sharp image of the object is formed on the screen adjacent to the object. When this has been done both object and image are at the same distance from the

mirror, and hence both must be situated in a plane passing through the centre of curvature and at right angles to the axis. The distance between mirror and screen is measured. Half this distance is the focal length of the mirror.
Method (2). Using a pin at C. The concave mirror is supported vertically in a suitable holder, and a pin, stuck in a cork held in a clamp and stand, is adjusted so that the tip of the pin is at the same level as the centre of the mirror. The pin is then moved along the bench in front of the mirror until a real inverted image of the pin is seen somewhere in front of the mirror. If necessary, the tilt of the mirror should be adjusted until the tip of the image is at the same level as the tip of the pin. The p in isthen moved to and fro until there is no parallax between the pin and its image. When this adjustment has been properly made the pin and its image will rema in in the same straight line when the eye is moved from side to side (see Fig. 22.17).

Sometimes the image is a little difficult to find, but this can usually be  overcome by making quite sure that the principal axis of the mirror passes through the tip of the object pin.

In experiments of this type one must resist a natural inclination to look into the mirror. The eye should be fixed on the pin, and the image will be seen to move backwards and forwards as the pin is moved to and fro. The pin is halted just when the image is exactly above it.

Hence, if u and v are measured we can calculate f Two pins are required, one to act as an object and the other as a search pin. The object pin is placed in front of the mirror between F and C so that a magnified real image is formed beyond C. The search pin is then placed so that there is no parallax between it and the real image (Fig. 22.18).

The distance of the object pin from the mirror will then give the object distance u, and that of the search pin the image distance v. Several pairs of object and image distances are obtained in this way and the results entered in a table as shown. A mean value for the focal length f may then be calculated. Care should be taken to apply correct arithmetical signs according to the sign convention used (see end of chapter).

The above method of calculation requires a. table of reciprocals, but if this is not available it will be found easier to calculate the focal length.