Which of the following relations is correct for a spherical mirror if a point object is kept on the principal axis ['P' is pole 'C' is centre object is at point 'O'. Image is at point 'I'].

Options

A. `(OP)/(OC)=(IP)/(IC)`
B. `(OP)/(IC)=(IP)/(OC)`
C. `(PC)/(PO)=(PI)/(PC)`
D. `(IO)/(CP)=(IP)/(CO)`

Answer

A

Explanation

In the figure shown

`because Delta OO' P` & `Delta II' P` are similar
`(OO')/(II') =(OP)/(IP)` ….(1)
also `because Delta OO'C` & `Delta II'C` are similar
`(OO')/(II')=(OC)/(IC)` ....(2)
By equation (1) and (2)
`(OP)/(IP)=(OC)/(IC) rArr (OP)/(OC)=(IP)/(IC)`.