Question

A flat circular mirror of radius 0.210 m is lying on the floor. Centered directly above the mirror, at a height of 0.660 m, is a small light source. Calculate the diameter of the bright circular spot formed on the 2.70 m high ceiling by the light reflected from the mirror.

Answer 1

Answer:

2.14 m

Explanation:

The mirror creates a virtual light source 0.66 m under it that is the reflection of the real one. This will project a cone of light on the ceiling. The cone of light will be delimited by the edges of the mirror.

When the cone has been projected 0.66 m (touching the mirror) it will have a diameter of 0.42 m. So when it gets projected on the wall, that is 2.7 + 0.66 = 3.36 m away, it will have a diameter of:

$\frac{0.42}{0.66} = \frac{x}{3.36}$

$x = \frac{0.42*3.36}{0.66} = 2.14 m$