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
- 5 cm
- -10 cm
- 20 cm
- -30 cm
Answer
(4) -30 cm
Solution
Without the lens the converging rays would meet at 15 - 5 = 10 cm from the lens position. For the lens this point acts as a virtual object on the right side.
u = +10 cm and v = +15 cm (sign convention: light travels left to right).
Lens formula: 1f = 1v - 1u
1f = 115 - 110 = 2 - 330 = - 130
f = -30 cm (negative, as expected for a diverging lens).
Answer: (4)