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When an object is placed at a distance of 25 cm from a mirror, the magnification is m1. the object is moved 15 cm away with respect to the earlier position, magnification becomes m2. if m1/m2 = 4,the focal length of the mirror is ?

When an object is placed at a distance of 25 cm from a mirror, the magnification is m1. the object is moved 15 cm away with respect to the earlier position, magnification becomes m2. if m1/m2 = 4,the focal length of the mirror is ?

Grade:12th pass

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
Let the object distance is do1 and do2
Let the image distance be d11 and d12

We know that 1/d0 + 1/d1 = 1/f

when do1 = -25cm

-1/25+1/d11=1/f ------1

-d11/25 = m1 --------2

When do2 = -40cm

-1/40 + 1/d12 = 1/f -------3

-d12/40 = m2 --------4

2/4
=>d11/d12 = 5/2
let d1=5x and d12=2x
1-3
=>1/d11 – 1/d12 = 1/25 – 1/40 = 3/200
=>1/5x – 1/2x = 3/200
=>x=-20

d11=-100

putting it in 1
we get f=-20m.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

 

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