(i) Calculate the distance of an objective of height h from a concave mirror of radius of curvature 20 cm , so as to obtain a real image of magnification 2. find the location of image also .
(iii) Using mirror formula explain Why does a convex always produce a virtual image .

Explanation

(a) Given focal length ` f = ( R ) /(2) = (20)/(2) = 10 cm`
Magnification `m = -(V)/(u) =-2`
`rArr " " v = 2u`
Using mirror formula `(1)/( f) = (1)/(v ) + (1)/(u) =-(1)/(10) =(1)/(2u) = (1)/(u) rArr (3)/(2u) =- (1)/(10)`
Also `underset( v = 2 u =-3- cm)(u=- 15 cm)`
(b) For a convex mirror f is positive for real object u is negtive
` (1)/(f) =(1)/(v) + (1)/(u) rArr (1)/(v) =(1)/(f ) -(1)/( u)`
au u is negative so `(1)/(v)` is positive i.e., v is positive from the equation i.e., image always lie belind the mirror . Hence image is always virtual.