Question

A section of a sphere is mirrored on both sides. If the magnification of an object is +4.80 when the section is used a concave mirror, what is the magnification of an object at the same distance in front of the convex side?

Answer 1

The magnification is given by,      m = - d_i / d₀

(+4.8) = - d_i / d₀

d_i = - 4.8 d₀

using a len's formula, we have

1 / d₀ + 1 / d_i = 1 / f

1 / d₀ - 1 / 4.8 d₀ = 1 / f

1 / f = 3.8 / 4.8 d₀

f = (4.8 d₀) / 3.8

f = 1.26 d₀

If we flip the mirror , then the new focal length will be given as :

f = - 1.26 d₀

Again, using a len's formula -

1 / d₀ + 1 / d_i = 1 / f

1 / d_i = -1 / (1.26 d₀) - 1 / d₀

1 / d_i = - (1.8) / d₀

d_i = - d₀ / (1.79)

Now, the magnification of an object at the same distance in front of the convex side which is given as :

m = - d_i / d₀ = [d₀ / (1.79)] / d₀

m = 0.557