- #1

- 594

- 12

## Homework Statement

Find an approximate expression for the ratio of the power densities at the principal maximum to that at the first secondary maximum on either side, in the Fraunhofer diffraction pattern of an N-slit multiple aperture. Assume that the slits are much narrower than their separation, and that the peak of the secondary maximum occurs halfway between the first and second zeros of the pattern (not exactly true).

## Homework Equations

The width of the central diffraction peak

[1] Diffraction minima: nλ=b sinθ

[2] Central interference fringe: pλ=a sinθ

where

a: width of slit

b: width of portion between slits

θ: angle of diffraction

λ: wavelength of light

p & n: both integers

## The Attempt at a Solution

Dividing [2] by [1]

pλ / mλ = p/n

a sinθ / b sinθ = a/b

so a/b = p/n

∴ 2(a/b) = ratio of widths of the central diffraction peak to the central interference fringe

Can this also be extended to the ratio of power densities of the Fraunhofer diffraction pattern? I can't really think of any other way to answer the question. Any help would be much appreciated.