Images from Spherical Mirrors — Question 7

Question 7

A convex mirror can form a real image of a virtual object

Use the paraxial mirror relations $1/p+1/q=1/f$ and $m=-q/p$, with p positive for a real object, q positive for a real image, and f positive for a concave mirror. A convex mirror has f=-20 cm. An incoming converging bundle would meet 10 cm behind the mirror if reflection did not occur.

1. Assign the signed object distance and calculate the reflected image distance.

2. Find magnification relative to the would-be object pattern and explain why the result does not contradict ordinary convex-mirror images.

Question 7 - Solution

A convex mirror can form a real image of a virtual object

(a) Method and calculation

$$\boxed{p=-10\,\mathrm{cm}}\quad\text{because the incident bundle is converging}.$$$$\frac1q=\frac1f-\frac1p=-\frac1{20}+\frac1{10}=\frac1{20}\Rightarrow\boxed{q=+20\,\mathrm{cm}}.$$

(b) Interpretation and further calculation

$$\boxed{m=-q/p=+2}.$$$$\boxed{\text{real reflected image of a virtual object}}.$$

Physical check

The usual statement that a convex mirror gives a virtual reduced image assumes a real object; that assumption is absent here.