Principle of Linear Superposition: When two or more waves are present simultaneously in the same region of space the resultant disturbance is the sum of the disturbances from the individual waves. Accordingly, two or more light waves can interfere constructively or destructively when they exist at the same place at the same time provided they originate from coherent sources. Two sources are coherent if they emit waves that have a constant phase relationship (wavelength, frequency, and position).
Young's Double-Slit Experiment: Young passed light through a pair of closely-spaced narrow slits. As a result he produced a pattern of alternating bright and dark fringes (bands) on a viewing screen. The images arise due to the constructive and destructive interference of the waves emanating from the overlapping sources at each slit. The following relationship holds:
lsource = dx/L
where d is the spacing between the slits (meters), x is the distance from the first bright fringe to the central maximum (meters) , and L is the distance from the slits to the screen (meters).
Similarly, the angle q for the mth high-order bright fringe is given by
sinq = m(lsource)/d
where d is the slit spacing (meters), m is 0, 1, 2, 3, ...., and q is the angle between the acute bisectrix and the lines drawn from a point midway between the slits to the respective bright fringes.
Similarly, the angle q for thedark fringes is given by
sinq = (m +0.5)(lsource)/d
Solve the following problems in the spaces provided or on a separate sheet of paper. Remember to employ proper problem-solving techniques throughout.
1. The transmitting antenna for a radio station is 7.00 km from your house. The frequency of the electromagnetic wave broadcast by this station is 536 kHz. The station builds a second transmitting antenna that broadcasts an identical electromagnetic wave in phase with the original one. The new antenna is 8.12 km from your house. Does constructive or destructive interference occur at the receiving antenna of your radio? (Show all work.)
2. In a Young's double-slit experiment, the angle that locates the second-order bright fringe is 2.0 degrees. The slit separation is 3.8 x 10exp(-5) m. Calculate the wavelength (l) of the light.