Why There Are No Pictures on Walls

The puzzle

A wall adds the light up

Imaging means blocking rays

Rooms are accidental cameras

A darkened room has one window, and a faint upside-down image of the outside forms on the far wall when most of the window is covered. Why does shrinking the opening produce a picture where the open window produced none?

Under the open window, a photometer reads a single intensity from one small patch of wall. According to the integral view of the previous steps, what can be concluded about the outside scene from this reading alone?

A matte wall patch has albedo $a = 0.5$. Two lamps deliver $\ell_{\text{in}} = 3$ units each, both arriving with the same geometry factor $\mathbf{n} \cdot \mathbf{p} = 0.4$. Lambertian reflection is linear in the incoming light. Compute the total reflected power as a decimal.