Young's Interference Experiment — Question 2

Question 2

A long fringe baseline reduces a wavelength measurement to one slope

In a paraxial double-slit experiment, $d=0.300\,\mathrm{mm}$ and $L=1.80\,\mathrm m$. The separation between bright orders $m=-4$ and $m=+6$ is $30.0\,\mathrm{mm}$. Ignore slit-width envelopes.

1. Infer the wavelength using the full measured baseline.

2. Find the nearest dark-fringe positions on either side of the positive second-order bright fringe.

Question 2 - Solution

A long fringe baseline reduces a wavelength measurement to one slope

(a) Method and calculation

$$y_6-y_{-4}=(6+4)\frac{\lambda L}{d}\Longrightarrow\lambda=\frac{d(30.0\,\mathrm{mm})}{10L}.$$$$\boxed{\lambda=500\,\mathrm{nm},\quad\Delta y=\lambda L/d=3.00\,\mathrm{mm}}.$$

(b) Interpretation and further calculation

$$y_{m+1/2}=(m+1/2)\Delta y;\quad y_2=6.00\,\mathrm{mm}.$$$$\boxed{y_{3/2}=4.50\,\mathrm{mm},\quad y_{5/2}=7.50\,\mathrm{mm}}.$$

Physical check

There are ten fringe intervals between orders minus four and plus six, even though eleven bright fringes are included.