(a) With the help pf a ray diagram , show how a concave mirror is used to obtain an erect and magnified image of an object .
(b) Using the ray diagram below , obtain the mirror formula and the expression for linear magnification.

Explanation

(a)
(b) `DeltaA'B'P~DeltaABP` (by A A similarity)
So , `(A'B')/(AB)=(B'P)/(BP)=(+v)/(-u)` . . . (i)
`DeltaA'B'C~DeltaABC` (by A A similarity)
So , `(A'B')/(AB)=(CB')/(CB)=(CP+PB')/(CP-BP)=(-2f+v)/(-2f-(-u))` . . . (ii)
From equation (i) and (ii),
`(+v)/(-u)=(-2f+v)/(-2f+u)`
`v(-2f+u)=-(-2f+v)`
`-2vf+4v=+2uf-uv`
`2uv=2uf+2vf`
Dividing by 2uvf,
`(1)/(f)=(1)/(v)+(1)/(u)`
From equation (i) , `(A'B')/(AB)=(-v)/(u)`
So, `(h_("i"))/(h_(0))=(-v)/(u)`
So, `m=(h_("i"))/(h_(0))=(-v)/(u)`