The distance between the candle and the collecting lens is 1.8 m, the focal length of the lens is 50 mm.

The distance between the candle and the collecting lens is 1.8 m, the focal length of the lens is 50 mm. Determine the distance from the candlestick image on the screen to the lens.

Given:
d = 1.8m = 180cm
F = 50mm = 5cm
Find: f =?
Decision :
1 / F = 1 / d + 1 / f (since the lens collecting signs remain)
1 / f = 1 / F-1 / d
1 / f = (d-F) / F * d
f = F * d / (d-F)
f = 5 * 180/175 = 5.14 cm (rounded to the nearest hundredth)
Answer: f = 5.14cm