Answer:
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.