Suppose you want to take a chest X-ray with an X-ray source that has a divergence of 2^o . If the film is 1 meters from the (point) source, how big is the spot size at the film in centimeters?

Convert 2 degrees to radians and multiply the result by 1 meter.

To determine the spot size at the film in centimeters, you need to use the concept of angular magnification. The spot size at the source can be related to the spot size at the film through angular magnification.

Angular magnification is given by the formula:

Angular magnification = (diameter at the source) / (distance from the source)

In this case, the divergence of the X-ray source is given as 2 degrees. This implies that the diameter at the source is 2 * 1 meter * (π/180) = 2π/90 meters.

The distance from the source to the film is given as 1 meter.

Using the formula for angular magnification:

Angular magnification = (2π/90 meters) / (1 meter) = 2π/90 radians

Now, to obtain the spot size at the film in centimeters, we need to multiply the angular magnification by the distance from the film.

Spot size at the film = Angular magnification * distance from the film

Spot size at the film = (2π/90 radians) * (1 meter) = 2π/90 meters

To convert the spot size to centimeters, we need to multiply by 100:

Spot size at the film = (2π/90 meters) * (100 cm/meter) ≈ 0.0707 cm

Therefore, the spot size at the film is approximately 0.0707 centimeters.