Question

Two students in a physics laboratory each have a concave mirror with the same radius of curvature, 50.0 cm. Each student places an object in front of a mirror. The image in both mirrors is three times the size of the object. However, when the students compare notes, they find that the object distances are not the same. What is the distance of the farther object?

Answer 1

One of the images is virtual while the other is real. If you know how images are formed by a concave mirror, we're looking for the real image in this case.
Since they haven't mentioned the sign of magnificatio in the question, the magnification could either be +3 or -3
-v/u= +/- 3

Now you know the mirror equation, 1/f = 1/v + 1/u
substitute the values one by one and you'll find the object distance required

case (I)

-v/u=3

1/-25=1/-u + 1/-3u

object distance , u=100/3

case (II)

-v/u=-3

1/-25=1/-u + 1/3u

object distance , u=50/3

Farther object is at 100/3

Thankyou

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