Images from Spherical Mirrors — Question 2

Question 2

An object inside the focal length produces an enlarged virtual mirror image

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 concave mirror has f=15 cm and an object at p=10 cm. The object height is 4 mm.

1. Find q and m and classify the image.

2. Find its height and the physical distance between object and image.

Question 2 - Solution

An object inside the focal length produces an enlarged virtual mirror image

(a) Method and calculation

$$q=15(10)/(10-15)=\boxed{-30\,\mathrm{cm}}.$$$$\boxed{m=-q/p=+3}\Rightarrow\text{virtual, upright, enlarged}.$$

(b) Interpretation and further calculation

$$\boxed{h_I=3(4)=12\,\mathrm{mm}}.$$$$\boxed{d_{OI}=p+|q|=40\,\mathrm{cm}}.$$

Physical check

The object and virtual image are on opposite sides of the mirror, so their physical separation is the sum of distance magnitudes.