Question

PROVE MIRROR FORMULA
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Answer 1

mirror formula is the relationship between

object

distance(u)image distance(v)abd focal lenght(f)

A ray of light starting from a and incient from mirror along ad parellel to the principle axis of the mirrir and get reflected from the mirror and passes through f.

another ray of light incident along ap is reflected along pa such that angle

apb=i

angle bpa =r

two reflected ray meet at a which is a real image ..

therefore ab is real, inverted image of ab formed by reflected from the mirror.

in trangle bac and abc

ab/ab=cb/cb........................(i)

now traingle abp and abp are similar

ab/ab=pb/pb.....................(ii)

from (i) and (ii)..........

cb/cb=pb/pb..................(iii)

measuring all distances by p we have......

cb=pb-pc

cb =pc-pb

therefore from (iii)

(pb-pc)/(pc-pb)=

pb/pb..................(iv)

convections..

pb=-u(distance of object)

pc=-r

pb=-v(distance of image)

we get from (iv).......

(-u+r)/(-u/-v)

or,

+ur-uv=uv-vr

or, ur+vr=2uv

dividing both side by uvr,

we get 1/v+1/u=2/r

as, r=2f

therefore,

1/v+1/u=2/r=2/2f=1/f

this is the required formula........

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