Question for Monday, September 26, hand in at beginning of class on paper

The figure above shows three different fields of view in the form of circular cones with different spreading angles $\theta$, lengths $R$ and diameters $D$.

The cones are thin enough so that $R \approx H$, where H is central length of the cone, and

$$sin \theta = \text{opposite/hypotenuse} \approx \theta = \frac{D/2}{R}$$

where D is the diameter of the cone.

Note that cones a) and b) have the same spreading angle $\theta1$ but different lengths $R1$ and $R2$, and that cones a) and c) have the same length $R1$ but different spreading angles $\theta1$ and $\theta 2$

Suppose the red line is a wall with uniform temperature emitting blackbody irradiance $E^*$. Find:

1) The irradiance E reaching a), b) and c) (the cone tips) assuming the power is spreading out into a hemisphere of radius $R$ in each case.

2) The radiance L = E/$\Delta \omega$ at a), b) and c).

If you do it right, you should find that the three radiances are identical, i.e. that for small angles and uniform emitters, L is independent of distance to the target.