Re: Pinhole Calculations

 Guillermo writes:

> Science tells us the radius an image point imaged by a small aperture is given
> by the formula:
>
> Image point radius = 0.61 * light_wavelength * focal_length / pinhole_radius

    Diffraction is not limited to small apertures like pinholes. Every lens or
    mirror that forms an image has diffraction. That means every camera or
    telescope. The largest telescopes, like the 200" (5 meter) mirror at Mt.
    Palomar still have diffraction.

    If we re-write the formula in terms of pinhole diameter instead of radius,
    we get:

        Image point radius = 1.22 * light_wavelength * focal_length
                              -------------------------------------
                                         pinhole_diameter

    Now notice that focal_length / diameter = f_number, so the formula becomes:

        Image point radius = 1.22 * light_wavelength * f_number

    At f 3.3, the Mt. Palomar mirror produces star images no smaller than
    .0022 mm in radius (for green light of 550nm wavelength).

    If there were no lens defects, if you photograph a star with your 35mm
    camera with a 50mm lens set to f 3.5, your star images will be almost
    exactly the same size as the star images produced by the 200" f 3.3 mirror
    of Mt. Palomar. Mt. Palomar, will however, put a lot more light into each
    of those star images because its collecting area is 122,500 times larger.
    And the scale of the image is different because Mt. Palomar has 16,764 mm
    focal length.
Received on Mon Mar 11 16:44:26 2002