Question

A concave spherical mirror with a radius of curvature of 100 cm creates an inverted image at a distance of 2.7 m from the mirror. Where is the object located?

61.4 cm from the mirror

2.85 cm from the mirror

159 cm from the mirror

5.70 cm from the mirror

42.2 cm from the mirror

Answer 1

The mirror's radius of curvature is R = 100 cm.

So, focal length of the mirror = f = R / 2 = 100 cm / 2 = 50 cm.

Focal length of a concave mirror is in front of the mirror, so it is negative.

So, f = - 50 cm.

Since the image is inverted, it must be real, hence, the image is in front of the mirror.

So, the image distance must be negative.

Hence, image distance = v = - 2.7 m = - 270 cm.

Hence, object distance u is given by :

1 / f = 1 / v + 1 / u

or, 1 / u = 1 / f - 1 / v = ( v - f ) / vf

or, u = vf / ( v - f ) = { ( - 270 ) x ( - 50 ) / ( - 270 + 50 ) } cm

or, u ~ - 61.4 cm.

Hence, the image of the candle is located 61.4 cm in front of the mirror's vertex.

So, correct option is : 61.4 cm from the mirror.