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 ?

Dear Student,
Let the object distance is d_o1 and d_o2
Let the image distance be d₁1 and d₁2

We know that 1/d₀ + 1/d₁ = 1/f

when d_o1 = -25cm

-1/25+1/d₁1=1/f ------1

-d₁1/25 = m1 --------2

When d_o2 = -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.