43. A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is ?

43. A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is ?

(a) −10 cm

(b) 20 cm

(c) −30 cm

(d) 5 cm

Answer :  (c) −30 cm

\( f = ? \quad (\text{negative concave}) \)

\( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \)

\( = \frac{1}{15} - \frac{1}{10} \)

\( = -\frac{1}{30} \)

\( f = -30 \ \text{cm} \)