Focal Length Of Convex Lens

NCERT Class 12, Chapter 9 provides the thin-lens equation $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$, used in the laboratory to find a convex lens focal length by measuring object and image distances. Applying the Cartesian sign convention, the object lies to the left so $u=-30$ cm, and the real image forms on the screen to the right so $v=+60$ cm. Substituting, $\frac{1}{f}=\frac{1}{60}-\frac{1}{-30}=\frac{1}{60}+\frac{1}{30}=\frac{1}{60}+\frac{2}{60}=\frac{3}{60}=\frac{1}{20}$, giving $f=20$ cm. The value 90 cm is wrong because it simply adds the object and image distances, which is not the focal length. The value 45 cm is wrong because it averages the two distances rather than combining their reciprocals. The value 10 cm is wrong because it doubles the reciprocal sum incorrectly. In the laboratory, several trials are taken with different object distances, and the focal length is either averaged or found graphically by plotting the reciprocal of image distance against the reciprocal of object distance, whose intercepts give the focal length. The parallax method is again used to locate the sharpest image before the distances are measured from the optical centre of the lens. A magnitude check confirms that a 20 cm focal length lens correctly produces a real image beyond twice the focal length when the object lies between f and 2f, consistent with the 30 cm object and 60 cm image geometry described.