A lens of focal length 20 cm forms the image of a bright object kept 30 cm from it on a screen. If the lens is replaced by another lens, the object has to be moved by 5 cm to obtain a sharp image on the screen. Find the possible values of the focal length of the second lens.

PLACEHOLDER ANSWER - the question has two answers. With the first lens, $$\frac{1}{v} = \frac{1}{20} - \frac{1}{30} = \frac{1}{60}$$, so the screen is 60 cm from the lens. With the object now at 25 cm or 35 cm, $$f = \frac{uv}{u + v}$$ gives $$\frac{25 \times 60}{85} = \frac{300}{17} \approx 17.6\text{ cm}$$ or $$\frac{35 \times 60}{95} = \frac{420}{19} \approx 22.1\text{ cm}$$.