Question

A concave mirror of focal length 18 cm forms an erect image, three times the size of the object, how far is the object from the mirror?​

Answer 1

Answer:

12 cm

Step-by-step explanation:

Given there is a concave mirror.

Focal length, f = -18 cm

Also, it's given that, it forms an erect image, three times the size of object.

Therefore, it will be a virtual image.

Therefore, we will get,

Object distance, u = -ve

Image distance, v = +ve

Now, we have,

Magnification, m = 3

But, we know that,

m = -v/u

Therefore, we will get,

=> -v/u = 3

=> v = - 3u

=> v = - 3u

Now, we know the mirror formula, i.e.,

1/u + 1/v = 1/f

Substituting the values, we get,

=> 1/u - 1/3u = -1/18

=> 3/3u - 1/3u = -1/18

=> (3-1)/3u = -1/18

=> 2/3u = -1/18

=> 3u/2 = -18

=> 3u = -18 × 2

=> 3u = -36

=> u = -36/3

=> u = -12

Therefore, we have,

=> v = -3(-12)

=> v = 36

Hence, the object is at a distance of 12 cm from the mirror.