Question

Establish the relationship between object distance,image distance and radius of curvature of a convex mirror.

Answer 1

easy by simple sign conversion

Answer 2

Answer:

(i) Let us consider an Object O' placed on the principal axis of a concave mirror (For your convenience, the mirror is drawn as Plane mirror but treatr the mirror as Concave mirror) of Focal length (F).

(ii) When, the object lies beyond the 'C', a real and Inverted image is formed between 'C' and 'F' after reflection from the Concave mirror.

(iii) From siliar triangles BO' A and BFP we can write the proportionalitites for corresponding sides as AB/PB = AO'/PF ⇒ AB/AO = PB/PF - (1)

From similar triangles $BO'A$ and $BFP$,

We can also write, AB/BI' = PA/PF - (2)

From Equation (1), (2),

= AB/AO' + AB/BI' = PB/PF + PA/PF

= AB/AO' + AB/BI' = PB + PA/PF = AB/ PF

= 1/AO' + 1/BF' = 1/PF

Using Cartesian Sign-convention,

AO' = Object Distance = -u

BI' = Image Distance = -v

PF = Focal Length = -f

∴ 1/-u + 1/-v = -1/f

∴ 1/u + 1/v = 1/f

∴ This is the Mirror formula.