Question

Calculate the image position and magnification for an object placed (a) 20cm and (b) 60 cm in front of a convex mirror of focal length 40cm
please answer this ​

Answer 1

Answer: see below in details

Explanation:

We know the mirror formula:

$\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$

Where u = object distance, v = image distance and f = focal length

(a) Given that,  u = -20 cm

focal length f = 40 cm

$\frac{1}{-20} + \frac{1}{v} = \frac{1}{40}\\\\or, \frac{1}{v} = \frac{1}{40} + \frac{1}{20}\\\\or, v = 40 / 3 cm= 13.333 cm$

So the magnification m = - v / u = 40/ (3 x 20) = 2/3

(b) Given that,  u = - 60 cm

focal length f = 40 cm

$\frac{1}{-60} + \frac{1}{v} = \frac{1}{40}\\\\or, \frac{1}{v} = \frac{1}{40} + \frac{1}{60}\\\\or, v = 120 / 5 ~cm= 24 ~cm$

So the magnification m = - v / u = 24 / 60 = 2/5