Summarizing Young’s Double Slit Experiment

Young’s Double Slit Experiment Summary

• Young’s double slit experiment gave definitive proof of the wave character of light.
• An interference pattern is obtained by the superposition of light from two slits.
• There is constructive interference when \(d\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =\mathrm{m\lambda }\phantom{\rule{0.25em}{0ex}}\text{(for}\phantom{\rule{0.25em}{0ex}}m=0,\phantom{\rule{0.25em}{0ex}}1,\phantom{\rule{0.25em}{0ex}}-1,\phantom{\rule{0.25em}{0ex}}2,\phantom{\rule{0.25em}{0ex}}-2,\phantom{\rule{0.25em}{0ex}}\dots )\), where \(d\) is the distance between the slits, \(\theta \) is the angle relative to the incident direction, and \(m\) is the order of the interference.
• There is destructive interference when \(d\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =(m+\cfrac{1}{2})\lambda \phantom{\rule{0.25em}{0ex}}\text{(for}\phantom{\rule{0.5em}{0ex}}m=0,\phantom{\rule{0.25em}{0ex}}1,\phantom{\rule{0.25em}{0ex}}-1,\phantom{\rule{0.25em}{0ex}}2,\phantom{\rule{0.25em}{0ex}}-2,\phantom{\rule{0.25em}{0ex}}\dots )\).

Glossary

coherent

waves are in phase or have a definite phase relationship

constructive interference for a double slit

the path length difference must be an integral multiple of the wavelength

destructive interference for a double slit

the path length difference must be a half-integral multiple of the wavelength

incoherent

waves have random phase relationships

order

the integer \(m\) used in the equations for constructive and destructive interference for a double slit