Finding a Wavelength from an Interference Pattern

The third bright line is due to third-order constructive interference, which means that $m=3$. We are given $d=0\text{.}\text{0100}\text{mm}$ and $\theta =\text{10}\text{.}\text{95º}$. The wavelength can thus be found using the equation $d\text{sin}\theta =\mathrm{m\lambda }$ for constructive interference.

The equation is $d\text{sin}\theta =\mathrm{m\lambda }$. Solving for the wavelength $\lambda$ gives

Substituting known values yields

To three digits, this is the wavelength of light emitted by the common He-Ne laser. Not by coincidence, this red color is similar to that emitted by neon lights. More important, however, is the fact that interference patterns can be used to measure wavelength. Young did this for visible wavelengths. This analytical technique is still widely used to measure electromagnetic spectra. For a given order, the angle for constructive interference increases with $\lambda$, so that spectra (measurements of intensity versus wavelength) can be obtained.