Young's Interference Experiment — Question 9

Question 9

Counting bright orders requires respecting the propagating-angle limit

Two ideal pointlike coherent apertures separated by $d=2.20\,\mu\mathrm m$ radiate at wavelength $\lambda=500\,\mathrm{nm}$. For normal illumination, bright orders satisfy $d\sin\theta=m\lambda$. Count only forward directions with $-90^\circ<\theta<90^\circ$. Ignore any aperture envelope.

1. Determine all allowed integer orders and the number of bright directions.

2. Find the largest positive bright angle and explain why the next order is absent.

Question 9 - Solution

Counting bright orders requires respecting the propagating-angle limit

(a) Method and calculation

$$|\sin\theta|<1\Longrightarrow|m|<d/\lambda=4.40.$$$$\boxed{m=-4,-3,\ldots,3,4;\quad N=9}.$$

(b) Interpretation and further calculation

$$\boxed{\theta_4=\sin^{-1}(4/4.4)=65.380^\circ}.$$$$m=5:\quad\sin\theta_5=5/4.4>1\Longrightarrow\boxed{\text{no propagating order}}.$$

Physical check

This is a geometrical existence limit, distinct from a bright order being suppressed by a finite-slit diffraction envelope.