A circular aperture is lit up by a laser with wavelength 538 nm. The central maximum on the screen 59.0 cm away has the same diameter as the circular aperture. What is the diameter of the circular aperture?
if w = diameter of slit
L = wavelength = 538 * 10^-9 meters
distance of first minimum from center = w/2
T is angle from straight ahead to first minimum
w sin T = 538*10^-9 /2 so sin T = 538*10^-9 /2w
w/2 = 0.59 sin T so sin T = w /(2* .59)
so
538*10^-9 /2w = w / (2*.59)
w^2 = .59 * 538*10^-9 = 317*10^-9 = 31.7 * 10*-10
w = 5.63 * 10^-5
w = 0.000053 meter