Question

Rohit placed a pencil perpendicular to principal axis in front of a converging

mirror of focal length 30 cm. The image formed is twice the size of the pencil.
Calculate the distance of the object from the mirror.

Answer 1

45cm

Step-by-step explanation:

A converging mirror is also known as a concave mirror. For a concave mirror, its focal length and the image distance are both positive.

Using the mirror formula as shown to get the object distance;

`(1)/(f) = (1)/(u) + (1)/(v)`

f is the focal length of the mirror

u is the object distance

v is the image distance

Given f = 30cm and v = 2u (The image formed is twice the size of the pencil)

Substituting this values in the formula to get u we have;

`(1)/(30) = (1)/(u) + (1)/(2u)\\(1)/(30) = (2+1)/(2u)\\(1)/(30) = (3)/(2u)\\`

Cross multiplying we have;

2u = 90

Dividing both sides by 2;

2u/2 = 90/2

u = 45cm

The distance of the object from the mirror is 45cm