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 of the concave mirror is, \(m=-\frac{q}{p}\)

Here, \(q\) is the size of the image and \(p\) is the size of the object The focal length is same for the mirrors. The focal length can be calculated using the lens formula as follows:

\(\frac{1}{f}=\frac{1}{p}+\frac{1}{q}\)

Thus,

$$ \begin{aligned} \frac{1}{f} &=\frac{1}{p}+\frac{1}{q} \\ \frac{1}{f} &=\frac{p+q}{p q} \\ f &=\frac{p q}{p+q} \end{aligned} $$

As the focal length of the two mirrors is Thus,

$$ \begin{array}{c} \frac{p q}{p+q}=\frac{p q^{\prime}}{p+q^{\prime}} \\ \frac{q}{p+q}=\frac{q^{\prime}}{p+q^{\prime}} \\ \frac{4.8 p}{p-4.8 p}=\frac{q^{\prime}}{p+q^{\prime}} \\ -1263=\frac{q^{\prime}}{p+q^{\prime}} \\ -1.263=\frac{q^{\prime}}{p+q^{\prime}} \\ -1.263 p-1263 q^{\prime}=q^{\prime} \\ \frac{q^{\prime}}{p}=-0.558 \end{array} $$

Thus, the magnification of the object at the same distance in front of the convex mirror is -0.558