I am trying to decide what lens should I use for eclipse and I am wondering if my 70-300 IS USM would be enough or should I get (rent) a lens with higher magnification. Since my solar filters are going to be only in a week, I was wondering, how can I determine how big the sun would be if I shoot at 300mm? What about at other focal lengths?
As Alan Marcus mentions, the sun (as well as the moon) are very close to the same size in the sky, at 0.5° of arc.
The angle of view 𝜃 of a lens with focal length ƒ, as seen by a camera with sensor size d, is given by:
𝜃 = 2 atan(d/2ƒ)
A Canon APS-C sensor is 22.2 mm wide by 14.8 mm tall. Using the short dimension of the sensor (the height), d = 14.8 mm. Therefore,
- at ƒ = 300 mm, 𝜃 = 2.83°, which is 2.83° / (0.5° per sun diameter) = 5.65 sun diameters across
- at ƒ = 400 mm, 𝜃 = 2.12°, which is 2.12° / (0.5° per sun diameter) = 4.24 sun diameters across
- at ƒ = 600 mm, 𝜃 = 2.12°, which is 1.41° / (0.5° per sun diameter) = 2.83 sun diameters across
With this approach, you can determine exactly how big the sun will be in your photo, depending on what focal length you use.
A very good resource is Fred Espenak's Mr. Eclipse pages, specifically How to Photograph a Solar Eclipse. That page specifically covers the size of the sun for different focal lengths, both on full frame and crop sensor cameras, as well as suggestions for focal lengths depending on what part(s) of the eclipse you are interested in shooting (solar disk, prominences, coronae, etc.).
With your camera and existing 70 - 300 lens, shoot pictures of the moon. The moon and sun appear in the sky as a disk, they image exactly the same as to size. Both are 1/2 degree of arc disks.
Addendum: Figuring out the size of the sun’s image is easy math. You can trace out a triangle from the edges of the sun to the camera lens. The image forming rays from the lens trace out a similar triangle inside the camera. Ratio to the rescue: The suns diameter is 864,576 miles. Sun’s mean distance from earth is 92,955,807 miles. The ratio diameter to distance is 92955807 ÷ 864576 = 0.00934.
The image forming rays of the camera lens trace out a triangle with this exact ratio. Thus if a 300mm lens is mounted, we multiply 300 X 0.00934 = 2.8. That tells us that if a 300mm lens is used , the image of the sun at film or digital sensor will be a circle 2.8mm in diameter.
We view the images of our miniature cameras by making an enlargement, be it print on paper or image on a computer monitor. To make an 8X10 print from a full frame (FX), the magnification requires a minimum of 8.5X. If this is the magnification, the final image of the sun will be 2.8 X 8.5 = 23.8mm (about 1 inch). If the camera is a compact (DX or APS-C), the magnification will be about 1.5X more --- thus 23.8 X 1.5 = 35.7mm (sun’s image diameter or about 1.4 inches).
I've found the following sentence in a 1999 NASA bulletin:
For any particular focal length, the diameter of the Sun's image is approximately equal to the focal length divided by 109.
Using this equation it gives 300/109 which is approximately 2.75mm.