Question

A concave mirror of radius of curvature 16 cm produces two-times enlarged real image of an object kept in front of it. Find the position of the object.

Answer 1

Given: Radius of curvature (R) = −16 cm (concave mirror)

Focal length (f) = `(-16)/2` = −8 cm

The image is real and enlarged two times, so m = −2    ...(magnification is negative for real images).

From m = `-v/u`,

−2 = `-v/u`

⇒ v = 2u

Now, using the mirror formula:

`1/f = 1/v + 1/u`

`1/-8 = 1/(2 u) + 1/u`

`1/-8 = (1+ 2)/(2 u)`

`1/-8 = 3/(2 u)`

2u = −24

u = −12 cm

∴ The object is placed at a distance of 12 cm in front of the mirror.