A photographer wants to take a picture of the Cape Byron lighthouse in the easternmost point of Australia with the full moon as background, but he wants the full moon and the lighthouse to be about the same size. The light house has a height of 22 meters, and the moon subtends an angle of about 0.53 degrees of arc to an observer on the Earth. How far from the lighthouse should the photographer place the camera to get the picture?
Using the following image as reference, we know that the height of the lighthouse, y, is 22 meters and that the angle θ has to be the same as for the moon, 0.53 degrees. The distance from the camera to the lighthouse is given by x. The trigonometric equation for the tangent of an angle is tan(θ) = y/x. Thus, x = y/tan(θ) = 22 meters/0.00925 = 2,378 meters. Note: When using a calculator for the tangent make sure to set it for degrees and not radians.
The photographer has to place the camera approximately 2.4 kilometers from the lighthouse.
This is what Luke Taylor had to say about his photograph:
The equipment I used to capture this was Canon 7D, Canon 600mm f/4 IS II & Canon 1.4 Extender giving me a focal length of 840mm but 1344mm if you take the cropped sensor of the Canon 7D into the equation. My location was 4.3 kilometers away from Cape Byron Lighthouse, on Belongil Beach, Byron Bay, New South Wales, Australia.
In order for the moon to look bigger than the lighthouse, the photographer positioned his camera almost twice as far from the lighthouse than in our problem.