The image formed by a convex mirror of focal length `30 cm`. is a quarter of the object. What is the distance of the object from the mirror ?

Options

A. `{:("Object Distance","Image Distance (v)"),("-90 cm","22.5 cm"):}`
B. `{:("Object Distance","Image Distance (v)"),("-22.5 cm ","+90 cm"):}`
C. `{:("Object Distance","Image Distance (v)"),("-90 cm","-22.5 cm"):}`
D. `{:("Object Distance","Image Distance (v)"),("-90 cm ","+90 cm "):}`

Answer

A

Explanation

It is given that focal length, `f=+30 `cm and size of image = `1/4`imes size of object. Therefore, `m = +1/4 = -v/u`
`implies u = -4v`
Applying the mirror formula,
`1/f = 1/v + 1/u`
`= 1/30 = 1/v - 1/(4v) `
`= (4 - 1)/(4v) = 3/(4v)`
`implies v = + 90/4`
`= 2.25 cm`
`u = - 90 cm`