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Question:

In an experiment a convex lens of focal length 15cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20cm from the lens. The focal length of the convex mirror is: 27.5cm, 25.0cm, 30.5cm, 20.0cm

27.5cm

20.0cm

25.0cm

30.5cm

Solution:

for convex lens: u = -20cm, f = 15cm
1/v - 1/u = 1/f
1/v = 1/f + 1/u
1/v = 1/15 + (1/-20)
v = -60cm
for mirror: u = 55cm, f = ?
for the mirror to form image at 'O': u = R = 2f
f = R/2 = 27.5cm