experiment 15: THE FOCAL LENGTH OF A CONVEX LENS

Experiments to measure the focal length of a converging lens





Method (1). Using an illuminated object and plane mirror. The lens is set up in a suitable holder with a plane mirror behind it so that light passing through the lens is reflected back again (Fig. 24.12). The object used is a hole and cross-wire in a white screen illuminated by a pearl electric lamp.






Method (2). Using a pin and plane mirror. In this method the object consists of a pin set vertically in a special carrier or simply stuck in a cork held by a clamp and stand. Having adjusted the pin so that its tip is at the same horizontal level as the centre of the lens, a position is found for which there is no parallax between it and the real image formed (Fig. 24.13). For best results, attention should be given to the tilt of the plane mirror so that the tip of the image and the tip of the object pin appear to touchThe position of the lens holder is adjusted until a sharp image of the object is formed on the screen alongside the object itself. The object will now be situated in the focal plane of the lens, i.e., a plane through the principal focus at right angles to the principal axis. Under these conditions, rays from any point on the object will emerge from the lens as a parallel beam. They are therefore reflected back through the lens and brought to a focus in the same plane as the object. The distance between lens and screen now gives the focal length of the lens.







at the same level as the centre of the lens. The distance between pin and lens will then be equal to the focal length of the lens. Method (3). Measurement of object and image distances. The lens is set up in front of an illuminated object so that a real image is formed on a white screen placed on the opposite side (Fig. 24.14). Having adjusted the lens so that the image is sharply in focus, the object distance u and the image distance v from the lens are measured.



shown. A mean value for the focal length f may then be calculated. Instead of using an illuminated object, a pin may be set up in front of the lens so that it forms a real image on the opposite side. The position of this image is then located by the aid of a search pin, using the method of no-parallax

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Determination of the Length of a Convex Lens by the Displacement Method Apparatus Illustrated object ( e.g ‘ light box’), metre  rule,  convex lens, lens stand, screen.

 Method The screen is placed a measured distance D from the light‐box. The lens plated in between the object and the screen and a position is which a clear image is brown on the screen.   The position in which the lens stand is noted. Now keeping the object and screen fixed, another position is found in which the gives a well‐focused image on the screen. The distance d through which the lens is moved from its original position to the new position is measured. The focal length is determined from the measurements of d and D. the experiment is repeated with difference values of D and average value of f found. Theory let the distance between object and screen be D, and the displacement distance between the two positions of the lens be d. 16 Let u1, v1 and u2, v2 be the respective object and image distance in the two position, Hence O and I are conjugate points, it is clear that     u1=v2 and u2=v1 now u1+v1=D and v1‐v2= Note The advantage of this method of finding f that only measurements of precise distances are involved in the expression for f. the avoids the uncertainty always present u and v determinations of estimating the position of the optical centre of the lens.