The Rayleigh Criterion for resolution states that two point sources are just resolved when the
central maximum from one source falls on the first minimum of the diffraction pattern from the
other source. If a car is approaching you at night with headlights 1 meter apart, how far away
must you be in order to just resolve them? (Treat the headlights as single slits of width 1 mm,
and assume the lamps are monochromatic sodium sources of wavelength 589.29 nm).
Scientists use laser range-finding to measure the distance to the moon with great accuracy. A
brief laser pulse is fired at the moon, then the time interval is measured until the “echo” is seen
by a telescope. A laser beam spreads out as it travels because it diffracts through a circular exit
as it leaves the laser. In order for the reflected light to be bright enough to detect, the laser spot
on the moon must be no more than 1 km in diameter. Staying within this diameter is
accomplished by using a special large-diameter laser. If  = 532 nm, what is the minimum
diameter of the circular opening from which the laser beam emerges? The earth-moon distance
is 384,000 km.