An object is placed `18 cm` in front of a mirror. If the image is formed at `4 cm` to the right of the mirror, calculate its focal length. Is the mirror convex or concave ? What is the nature of the image ? What is the radius of curvature of the mirror ?

Options

A. 5.14 cm ; convex, erect and real ; 10.28 cm
B. 5.14 cm ; convex, diminished and virtual ; 10.28 cm
C. 5.14 cm ; concave, erect and real ; 10.28 cm
D. Edit 5.14 cm ; convex, erect and virtual ; 10.28 cm

Answer

D

Explanation

Here, `u = - 18 cm, v = 4 cm, f = ?, R = ?`
As `(1)/(f) = 1/u + (1)/(v), (1)/(f) = (1)/(-18) + 1/4 = (-2+9)/(36) = 7/36` or `f = 36/7 = 5.14 cm`
as f is +, therefore, mirror is convex. Image is virtual, erect and smaller in size.
`R = 2 f = 2 xx 5.14 = 10.28 cm`.