A real image three times the size of an object is formed 24cm from a converging mirror. What is the focal length of the mirror?

A. 16cm
B. 6cm
C. 8cm
D. 12cm

Correct Answer:

Option B – 6cm

Explanation

For a real image 3 times the size of the object, it implies that the magnification 3 = v/u, 3 = 24/u, therefore 3u = 24, u = 8cm thus we have from the relation:m = (f)/(u)-f; that 3 = (f)/(8) – f. therefore f = 3(8-f) f = 24 – 3f ∴4f = 24; f = 6cm OR: (1)/(u) + (1)/(v) = (1)/(f).
(1)/(8) + (1)/(24) = (1)/(f)
therefore (3+1)/(24) = (1)/(f)
4/24=1/f;therefore 4f = 24
f = 6cm