A candle is placed 17.0 cm in front of a convex mirror. When the convex mirror is replaced with a...

Question:

A candle is placed 17.0 cm in front of a convex mirror. When the convex mirror is replaced with a plane mirror, the image moves 6.0 cm farther away from the mirror. Find the focal length of the convex mirror. _cm

Convex Mirror vs Plane Mirror:

Both plane mirror and convex mirror forms virtual and upright image of the real objects. The image formed is behind the mirror. The convex mirror forms diminished image while the plane mirror forms image of same size as the object.

Given Data

• Distance of candle (object) from the convex mirror, u = 17.0 cm
• shift of image after replacing convex mirror with plane mirror, d = 6.0 cm

Finding the focal length (f) of the convex mirror

Since image formed by plane mirror is equidistant from the mirror as the object distance, therefore image distance from the plane mirror will be 17.0 cm

Therefore, since shift of image after replacement of convex mirror by plane mirror is d = 6.0 cm, the image distance from the convex mirror is:

• Image distance from convex mirror, v = -( 17 cm - 6.0 cm) = - 11 cm (with sign convention)

Applying mirror equation:

• {eq}\dfrac{1}{v}\ + \dfrac{1}{u}\ = \dfrac{1}{f} {/eq}
• {eq}\dfrac{1}{-11}\ + \dfrac{1}{17}\ = \dfrac{1}{f} {/eq}
• {eq}f\ = -31.2\ cm{/eq}