Shouldn't the diameter of the moon with a 600mm lens be double what it is with a 300mm lens?

Question

I used a 300 mm lens and recently bought a 600 mm lens, thinking that the area in the frame with the 600 mm lens will be exactly half of the area covered by the 300 mm lens. Practically I am not getting this; in fact very little difference. Should the diameter of the moon captured by a 600 mm lens be double the diameter of the moon captured by a 300 mm lens?

Answer 1

Assuming both lenses are being used on the same size sensor, the area in the frame with a 600mm lens should be one quarter the area in the frame with a 300mm lens. The linear dimensions should change by a factor of two, the areal dimensions should change by a factor of the square of two, which is four.

If you are not seeing the same object shot from the same distance appear to be twice as wide using the 600mm lens as with the 300mm lens then something else is going on here.

1. One or both of the two lenses may not be labeled properly. The chances are probably greater that the 600mm lens is not really 600mm than that the 300mm lens is appreciably longer than 300mm.
2. You are using a Nikon full frame (FX) camera and the 300mm lens is a Dx lens. When a Dx lens is attached to an FX camera the camera will automatically crop the image to only use the center of the FX sensor - the part that is completely covered by the smaller light circle of the Dx lens. This will give a field of view with the 300mm lens that is closer to the FoV of a 450mm lens with an image circle large enough to cover the entire sensor. Look at the resolutions of the photos using the two lenses. Are they the same? Or is the image with the 300mm lens much smaller in terms of pixels than the image with the 600mm lens?

Answer 2

The camera lens acts just like a movie or slide projector lens in that it projects an image on film or sensor. We can use the geometry associated with tringles to calculate the projected image size of the moon. The moon’s mean distance is 384,400 kilometers and its diameter is 3,474 kilometers. The ratio of distance to diameter is 384400 ÷ 3474 = 0.0090. In other words, our view of the moon traces out a triangle with a ratio of 0.0090 diameter to distance.

The camera lens projects an image of the moon and the image and the image forming rays trace out a triangle that tracks with the same ratio of distance to diameter. If a 300mm lens is mounted, this will be the distance lens to image. The diameter of the image will have the same ratio as the actual view. Thus we multiply 300 x 0.0090 = 2.71. We have calculated the diameter of the moon’s image, it is 2.71mm.

If we mount a 600mm lens we can recalculate 600 x 0.0090 = 5.40. The moon’s image using the 600mm is 5.40mm in diameter which is twice the size of the image formed by a 300mm.

By the way, the focal length of a lens is measured when the lens is imaging a far distant object (an object said to be a an infinite distance symbol ∞). This measure is taken from a point called the rear nodal. If the lens has a super simple design, the rear nodal is likely near the center of the lens array. A true telephoto differs from a simple long lens. It is constructed using a array of positive and negative lens elements and likely the barrel is artificially shortened by a clever element arrangement. Commonly, to make the lens barrel less unwieldy, the rear nodal is shifted far forward of center. In many cases it falls in air ahead of the lens. Nevertheless it preforms, as to magnification, exactly as if it were a simple lens. In other words a 600mm lens is a 600mm lens and a 300mm is a 300mm. The 600mm delivers twice the magnification.