Two Types of Image — Question 10

Question 10

A pinhole forms a real image without focusing by refraction or reflection

An object arrow of height h stands distance p before a small pinhole. A screen is distance q behind the hole. Light travels in straight lines; the hole is small enough to neglect geometrical blur, and diffraction is excluded.

1. Derive the signed image height from similar triangles and classify the image.

2. For p=1.2 m, q=0.18 m, and h=0.20 m, find image height and the screen distance needed to double its magnitude.

Question 10 - Solution

A pinhole forms a real image without focusing by refraction or reflection

(a) Method and calculation

$$\frac{h_I}{q}=-\frac{h}{p}\Rightarrow\boxed{h_I=-qh/p,\quad m=-q/p}.$$$$\boxed{\text{real, inverted image on the screen}}.$$

(b) Interpretation and further calculation

$$\boxed{h_I=-0.18(0.20)/1.2=-0.030\,\mathrm m}.$$$$|h_I|\propto q\Rightarrow\boxed{q_{\mathrm{new}}=0.36\,\mathrm m}.$$

Physical check

The pinhole selects narrow bundles instead of redirecting them. Image formation and optical focusing are not identical operations.