Question

derive mirror formula that is one divided by f is equal to 1
/u + 1 /v​

Answer 1

In ABC and A1B1C

<ABC = <A1B1C (right angles)

<ACB = <A1CB1

<CAB = <CA1B (common angle)

ABC is similar to A1B1C

AB/A1B1 = BC/B1C........(1)

similarly DEF issimilar to A1B1F

DE/A1B1 = EF/B1F....(2)

But DE = AB and when the aperture is very small EF = PF

Equation (2) becomes�

AB/A1B1 = PF/B1F....(3)

Frm equations (1) and (3) get

PF/B1F = BC/B1C

PF/PF-PB1 = PB + PC/PC - PB1

f/f - v = -u + 2f/2f - v

[PF = f, PB1 = v, PB = u, PC = 2f]

2(2f - v)= (f-v)(2f-u)