Question

A spherically mirrored ball is slowly lowered at New Years Eve as midnight approaches. The ball has a diameter of 8.0 ft. Assume you are standing directly beneath it and looking up at the ball. When your reflection is half your size then the mirror is _______ ft above you.

Answer 1

The distance between mirror and you is 2 ft.

Step-by-step explanation:

diameter, d = 8 ft

radius of curvature, R = 4 ft

magnification, m = 0.5

focal length, f = R/2 = 4/2 = 2 ft

let the distance of object is u and the distance of image is v.

`(1)/(f)=(1)/(v)+(1)/(u)\\\\(1)/(2)=(1)/(v)+(1)/(u)\\\\v = \frac {2 u}{u - 2}`

Use the formula of magnification

`m = (v)/(u)\\\\0.5 =\frac { u}{u - 2}\\ \\u - 2 = 2 u \\\\u = -2 ft`