Correct Answer: −15

Explanation

Since the image is real and magnified, the mirror used must be a concave mirror.

Magnification for mirror is given by

m = −v / u

Given that the image is three times magnified,

m = −3

So,

−v / u = −3

v = 3u   ...(1)

The distance between object and image is 40 cm.

For a real image formed by a concave mirror, object and image lie on the same side of the mirror, so

|v − u| = 40

Substitute v = 3u,

|3u − u| = 40

2|u| = 40

|u| = 20

Since object distance is negative,

u = −20 cm

From (1),

v = 3u = −60 cm

Now apply mirror formula,

1/f = 1/v + 1/u

1/f = 1/(−60) + 1/(−20)

1/f = −1/60 − 3/60

1/f = −4/60

f = −15 cm

Hence, the focal length of the mirror is −15 cm.

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