Finding the focal length
Steve McCurry is a celebrated photographer who specialises in stunning colour work in india, Afghanistan and Pakistan. On page 153 of his book South Southeast is a nice evening shot of a junction in old Bombay (aka Mumbai). The photo includes a tiny lunar disc just before full. Steve McCurry uses 35mm format film (or did, he may have gone digital by now…)
The Moon’s disc is 0.5 degrees across. The disc has a diameter of about 3.5 mm on the page, so 7mm on the page corresponds to one degree of angle.
The image is roughly 360 by 240 mm (10x reproduction). Pythagoras suggests
- √ (3602 + 2402) = 433mm as the diagonal measurement.
Dividing this diagonal measurement by 7mm gives 62 degrees (roughly) as the angle of view of the photo. This corresponds closely to the angle of view of a 35mm lens on 35mm film.
To calculate the angle of view (at ‘infinity’ – that means anything over three to five feet for most moderate focal length lenses) you just…
- Take half the diagonal of the film format (√ (362 + 242) = 43.3mm /2 = 21.5mm for 35mm film)
- Divide this by the focal length of the lens (21.5 mm / 35mm = 0.6143)
- This is the tan of half the angle of view, so
- Multiply the Inverse Tangent (tan-1(0.6143)) by 2 to find the angle of view
- I get this to be 2 * tan-1(0.6143) = 63.1 degrees
This formula is based on taking half the diagonal to be the opposite side of a right angled triangle, and the focal length of the lens to be the adjacent side of the right angled triangle. The image is formed at a distance corresponding to the focal length only if the lens is focussed at ‘infinity’.
Now, on Steve McCurry’s picture, the image of the Moon is about 90mm above the horizon as judged by the building line at the end of the street that recesses into the distance. As Bombay is a coastal city and is mostly built on reclaimed land, we can estimate the altitude of the Moon as roughly 90 / 7 = 13 degrees. The phase of the Moon is just past full and getting on for third quarter. The parallactic angle of the disc is very roughly 225 degrees from the Zenith. The last rays of the Sun are shining from behind the photographer (camera pointing roughly East). The image was taken in 1994. There can’t be many combinations of date and time that fit those constraints… watch this space.