Does focal length correlate to the required ND filter in sun photography?

Question

I got my hands on an M42 500mm lens and want to try sun photography. I also have a 2x and a 3x converter, thus I'm able to get a focal length range of 500-3000mm. Back in the day I bought a Baader AstroSolar DIY filter that is listed as ND3.8 (1/6300) that is approved for sun photography. The question is, does the focal length correlate to the required ND filter? Do you need a higher ND-value with higher focal lengths? The sensor's crop factor is 5.5 but that shouldn't make a difference here as it doesn't affect the light going through the lens and converter(s), right?

Is it safe (lens and sensor safe) to use above mentioned Baader ND3.8 filter with focal lengths up to 3000mm? The camera does not have an optical viewfinder, I'm not exposing my naked eye to the sun.

Answer 1

That filter should be safe with any lens that has the correct filter thread or to which it can be securely mounted and fully cover the entrance pupil.

One common misconception is that a longer lens concentrates more light; in fact, it's the other way around. A longer focal length makes a larger solar image on the sensor, therefore that image is dimmer (for lenses with similar entrance pupil diameter). The figure of merit here is the old f/ ratio. An f/8 lens at 100 mm will give the same image brightness as an f/8 lens of 20 mm, or one of 500 mm focal length.

Generally, the only concession you need to make for a longer lens is that, for a given focal ratio, the longer lens will have a larger filter mounting ring.

BTW, don't forget that your 2x converter costs you two stops of exposure (f/8 becomes f/16), the 3x costs three and a third (f/8 becomes f/24); combined, an f/8 lens is now f/48. With digital, your camera will meter through the lens, so you shouldn't need to manually compensate, but you need to be aware (in part, of why that combination isn't used much). You'll also give up some image quality with each converter, as well as lose a bit of contrast from the increased number of glass-air and glass-glass surfaces.

Answer 2

The accepted wisdom is that ND 3.8¹ is the minimum needed for CCD exposure to the sun through telephoto lenses without risk of electronic damage. One can probably safely assume that ND 3.8 is also sufficient for CMOS sensors, because in general CMOS sensors are less susceptible to heat damage than CCD sensors are.

_{¹ Be careful not to confuse ND 3.8 (an ND.number), which is a reduction factor of 1/6310, with ND3.8 (an NDnumber), which is only a reduction factor slightly more than 1/4. (ND4 is 1/4, ND2 is 1/2. On the other hand, ND 4 is 1/10000, ND 2 is 1/100). ND 3.8 = ND6310.}

Having said that, I'd be a little hesitant to go past around 1200mm without the use of teleconverters and assume it would still be safe for the sensor. The reason being that 1200mm at f/5.6 is the longest "standard" focal lengths that have been historically offered by both Canon and Nikon or any other camera and lens maker for 135 format sized cameras. Thus the accepted standard of ND 3.8 could be based on an entrance pupil of 210mm with the exit pupil just large enough to cover a full frame sensor (or 135 format film gate) with an image circle slightly larger than 43mm.

While it is true that the size of a sensor does not affect the amount of energy per unit area, the size of the entrance pupil does affect how much total energy is allowed into the lens. For longer focal length lenses with the same maximum aperture, the entrance pupil is necessarily larger. If all of that higher energy is projected onto the sensor, bad things can happen.

In your case, using a TC (or three) with a 500mm lens does not increase the size of the entrance pupil, it reduces the f-number and spreads the same amount of energy coming through the lens over a wider exit pupil. But the next person who reads this might not realize that if they've got a fairly "fast" telescope with a very large primary mirror that concentrates the total energy collected into an image circle the size of a small sensor, ND3.8 might not be enough. An A4 size sheet of Baader film can cover up to an eight inch telescope.

I was just worried about the highly collimated light on the sensor's surface and the possible heat inside the lens affecting the aperture.

Please be sure you're placing the filter in front of the entire lens. Some longer focal length lenses have drop-in filter holders near the back of the lens. Here's what happens to a lens when one places the solar filter in the drop-in slot behind the aperture diaphragm:

You can read the full story of this lens and cameras damaged by solar heat at this lensrentals.com blog entry about equipment damaged during the "Great American Eclipse" in 2017.