The image of the object can be located on the screen for two positions of convex lens such that u and v are exchanged. The separation between two positions of the lens is x = 20 cm. It can be observed from figure. $u_1 + v_1$ = 90 ...(i) $v_1 - u_1$ = 20 ...(ii) Solving equation (i) and equation (ii) $v_1$ = 55 cm, $u_1$ = 35 cm Now lens formula, $\frac{1}{v} - \frac{1}{u}$ = $\frac{1}{f}$ $\frac{1}{55} - \frac{1}{-35}$ = $\frac{1}{f}$ or $\frac{1}{55} + \frac{1}{35}$ = $\frac{1}{f}$ $\frac{35+55}{55 \times 35}$ = $\frac{1}{f}$ or f = $\frac{55 \times 35}{90}$ = + 21.38 cm