Your artist friend is designing an exhibit inspired by circular-aperture diffraction. a pinhole in a red zone is going to be illuminated with a red laser beam of wavelength 670 nm, while a pinhole in a violet zone is going to be illuminated with a violet laser beam of wavelength 410 nm. she wants all the diffraction patterns seen on a distant screen to have the same size.

for this to work, what must be the ratio of the red pinhole's diameter to that of the violet pinhole?

dred/dviolet=?

The minimum angle, I, of a light beam diffraction pattern from a circular aperture distance, D, can be calculated using the Rayleigh' criterion given as:

Explanation:

Now the min angle of the red light zone diffraction pattern will be;

 . . . . . . . . . . . . . . . . . . . .  Eqn 1

Similarly, the min angle of the violet light zone diffraction pattern will have;

 . . . . . . . . . . . . . . . . . . . Eqn 2

However, remember that, we were told that the diffraction patterns seen on the distant screen have the same size. This means that the two diffractions have the same min angle, i

i.e, I1=I2=I

By this, we can then find the ratio of the pinhole diameters (D1 and D2) of each apertures.

Comparing Eqn 1 and 2 gives,

Hence, it means that the ratio of the red pinhole diameter D1, to that of the violet pinhole D2, must be 1.633 for the diffraction patterns to work.

see earlier