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

Answer 1

We can use the mirror equation to solve this problem. The mirror equation is:

1/f = 1/di + 1/do

where:
f = focal length of the mirror (= -20 cm for a concave mirror)
di = distance of the image from the mirror
do = distance of the object from the mirror

Given that the image formed is three times the size of the object, we can conclude that di/do = 3.

Substituting these values into the mirror equation, we get:

1/-20 = 1/di + 1/do
-1/20 = 1/di + 1/do
-1/20 = (do + di)/(do*di)
-do*di/20 = do + di

Since di/do = 3, we can substitute di = 3do into the equation:

-do*(3do)/20 = do + 3do
-3do^2/20 = 4do
-do^2/20 = 4
do^2 = -80

This is not a possible solution, as the square of a real number cannot be negative.

Therefore, there are no real solutions to this problem.