Question

1. A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved further from the mirror.


Can you answer this question

Answer 1

Answer: Image at + 6.67 cm, m = + 0.55.

Explanation:

O = + 4.50 cm

u = - 12.00 cm

f = + 15.00 cm

We know the mirror formula:-

1/f = 1/v + 1/u

=> 1/v = 1/f - 1/u

=> 1/v = 1/15 - 1/(- 12)

=> 1/v = 1/15 + 1/12 = (4 + 5)/60

=> 1/v = 9/60

=> v = 60/9 = + 20/3 cm or + 6.67 cm.

We also know,

m = - v/u = - (20/3)/(- 12) = 20/36 = + 0.55.

Also when it is pushed forward gradually, the image maintains its erectness and virtual nature but the image becomes shorter.

[Remember the spoon experiment or metallic spheres which you often see in your home.]

Extra Shots:-

• Power of lens is defined by the reciprocal of its focal length: P = 1/f.
• Power of combination of lenses: P = P1 + P2 + ... = 1/f1 + 1/f2 + ... .
• Power of a pair or a system of two lens kept at a distance d : P = 1/f1 + 1/f2 - d/f1f2.