A pinhole camera is placed between an object and a sensor. Recall that images from a pinhole camera are inverted (see figure below). Assume that the object lies on a plane. Also assume that the plane containing the object, the plane containing the pinhole and the sensor plane are all parallel to each other.
- Show that straight lines are projected to straight lines. In particular, show that if $A, B, C$ are three collinear points on an object, then their corresponding images $a, b, c$ are also collinear.
- Suppose two identical objects $M$ and $N$ having height $60 \text{ cm}$ are placed before the pinhole camera at distances $90 \text{ cm}$ and $120 \text{ cm}$ respectively. Suppose also that the distance between the pinhole and the sensor plane is $30 \text{ cm}$. What are the heights of their images after projection through the pinhole camera?
