Question

A virtual image is formed 26.9 cm from a concave mirror having a radius of curvature of 48.1 cm. Determine the object distance.

Answer 1

Answer:

The object distance is -12.7 cm.

Explanation:

The sign of the image distance should be positive as the image formed is virtual. Virtual images are formed always on the backside of a concave mirror. The sign of radius of curvature of a concave mirror is always negative.

The radius of curvature, R = -48.1 cm

∴ Focal length, f = R/2 = -48.1 / 2 = -24.05 cm

Image distance, v = +26.9 cm

The distance of the object can be found using the mirror formula.

1/f = 1/u + 1/v

⇒ u = vf / (v - f)

    u = (+26.9 × -24.05) / (+26.9 - - 24.05)

    u = -646.94 / 50.95

    u = -12.7 cm

We can see the negative sign in the object distance. This sign shows that the object is on the left side of the mirror at a distance of 10 cm.