Chapter 37: Interference of Light (Electromagnetic) Waves In Chap. 18 (PHYS 1211), we studied the superposition of waves and interference We applied these concepts to sound waves and standing waves Here we will apply, and extend, these concepts to light waves - a field of study known as Physical Optics, where the wave properties of light become more apparent So, please review sections 18.1-3

Consider two waves with the same wavelength  moving in the same medium (n, f, v all the same) We make the additional condition, that the waves have the same phase – i.e. they start at the same time  Constructive Interference The waves have A1=1 and A2=2. Here the sum of the amplitudes Asum=A1+A2 = 3 (y=y1+y2) Sum A2 A1

If A1=A2, we have complete cancellation: Asum=0 If the waves (1= 2 and T1=T2) are exactly out of phase, i.e. one starts a half cycle later than the other  Destructive Interference If A1=A2, we have complete cancellation: Asum=0 A1 y=y1+y1=0 sum A2 These are special cases. Waves may have different wavelengths, periods, and amplitudes and may have some fractional phase difference.

Here are a few more examples: exactly out of phase (), but different amplitudes Same amplitudes, but out of phase by (/2)

To “add” the waves, we apply the Principle of Superposition: “When two (or more) waves overlap, the resultant wave “magnitude” at any point in space and time is found by adding the instantaneous “magnitudes” that a would be produced at that point by the individual wave if each were present alone.” Consider two point sources S1 and S2 separated by some distance

Young’s Double Slit Experiment Consider a plane wave of wavelength  incident on an opaque barrier with an opening of size D If D >> , the rays continue in a straight line (ray approx. is valid) If D << , the plane wave diffracts through the opening creating spherical waves in all directions.

For convenience, we place a screen at L The divergence of the light ray from its original path is called diffraction (see chap. 38) Now consider a barrier, but with two small slits (D << ) and a slit separation give by d (Young’s double slit experiment - 1801) The slits produce two point light sources, S1 and S2 – spherical waves, same , and in phase  two coherent light sources The two waves propagate over all space (right of barrier) and interfere over all space For convenience, we place a screen at L D>> D<<

A classic interference pattern is created on the screen The waves from the two sources interfere in exactly the same wave as for two point sources

Example Problem 1 Example Problem 2 Coherent light from a sodium-vapor lamp is passed through a filter which blocks everything except for light of a single wavelength. It then falls on two slits separated by 0.460 mm. In the resulting interference pattern on a screen 2.20 m away, adjacent bright fringes are separated by 2.82 mm. What is the wavelength? Example Problem 2 Two very narrow slits are spaced 1.80 m apart and are placed 35.0 cm from a screen. What is the distance between the 1st and 2nd dark fringes of the interference pattern when the slits are illuminated with coherent light of =550 nm?