Question

A 2.5cm candle is placed 12cm away from a convex mirror of focal length 30cm. Give the location of the image and the magnification
For class 10th

Answer 1

Given that,

Focal length (f) = 30 cm, object distance from the mirror (u) = -12 cm, height of object (ho) = 2.5 cm

We have to find the location of the image (v) and the magnification (m).

Now,

Mirror formula:

1/f = 1/v + 1/u

→ 1/30 = 1/v + 1/(-12)

→ 1/30 = 1/v - 1/12

→ 1/30 + 1/12 = 1/v

→ (2 + 5)/60 = 1/v

→ 7/60 = 1/v

→ 60/7 = v

→ 8.57 = v

Now,

m = -v/u

m = -8.57/(-12)

m = 8.57/12

m = 0.71

Also, using formula

m = hi/ho, we can find the image height.

0.71 = hi/2.5

0.71(2.5) = hi

1.775 = hi

(Height of image (hi) = 1.775 cm)

Therefore, the location of the image from the mirror is 8.57 cm and it's magnification is 0.71.