Question

15. An object is placed in front of a
concave mirror of focal length 20cm. The
image formed is 3 times the size of the
object. Calculate two possible distances of
the object from the mirror.​

Answer 1

FIRST CASE: When the image formed is virtual
magnification, m= -v/u
--> 3 = -v/u
--> v = -3u

According to the mirror formula,

--> 1/v + 1/u = 1/f
--> 1/-3u + 1/u = 1/-20
--> -1/3u + 3/3u = -1/20
--> 2/3u = -1/20
--> 3u = -40
--> u = -40/3
--> u = -13.3 cm

Thus, v = -3(-13.3) = 39.9

SECOND CASE: When image formed is real

magnification, m= -v/u
--> -3 = -v/u
--> v = 3u

According to the mirror formula,

--> 1/v + 1/u = 1/f
--> 1/3u + 1/u = 1/-20
--> 1/3u + 3/3u = -1/20
--> 4/3u = -1/20
--> 3u = -80
--> u = -80/3
--> u = -26.6 cm

Thus, v = 3(-26.6) = ~-80cm