Interaction light and substance. Thermal radiation bioobjects.

Wavefronts At a given time, a wave's "wavefronts" are the planes where the wave has its maxima. A plane wave's wavefronts are equally spaced, one wavelength apart. And they're perpendicular to the propagation direction.

A spherical wave is also a solution to Maxwell's equations. E(r,t) = (E0/r) Re exp i(kr – wt) where k is a scalar, and r is the radial co-ordinate. Unlike a plane wave, whose amplitude remains constant as it propagates, a spherical wave weakens. Its irradiance goes as 1/r2.

A plane wave impinging on a molecule scatters into a spherical wave. Scattering from an individual molecule is weak, but many such scatterings can add up--especially if interference is constructive.

Spherical waves often combine to form plane waves. A plane wave impinging on a surface will produce a reflected plane wave because all the spherical wavelets interfere constructively along a flat surface.

What happens to light when it encounters a surface? It is scattered by the surface molecules. But a beam can remain a beam if there is a direction for which constructive interference occurs. Constructive interference occurs for a reflected beam if the angle of incidence = the angle of reflection. Constructive interference occurs for a transmitted beam if the sine of the angle of incidence = sine of the angle of "refraction." (Snell's Law)

Refraction and Snell's Law AD = BD/sin(qi) AD = AE/sin(qt) So: BD/sin(qi) = AE/sin(qt) But: BD = vi Dt = (c0/ni) Dt & AE = vt Dt = (c0/nt ) Dt So: (c0/ni) Dt/sin(qi) = (c0/nt) Dt/sin(qt) Or: ni sin(qi) = nt sin(qt) qi qt

Snell's Law for many layers So we can ignore the intermediate layers!

Snell's Law explains many everyday effects The refractive index varies with density (and hence temperature)

Prisms disperse light Because the refractive index depends on wavelength, the refraction angle also depends on wavelength. Because n generally decreases with wave- length (dn/dl < 0), the shorter the wavelength, the greater the refraction angle. Differentiating implicitly w.r.t. l: Or: Prism dispersion

Rainbows result from refraction and reflection of sunlight in water droplets Note that there can be two rainbows, and the top one is inverted. And the sky is much brighter below the bottom one.

Rainbow explanation: Light in a spherical droplet Water droplet Light paths Light can enter a droplet at different distances from its edge. Path leading to minimum deflection ~180° deflection Minimum deflection angle (~138°); rainbow radius = 42° We must compute the angle of the emerging light as a function of the incident position.

Plotting deflection angle vs. wavelength is the key. Because n varies with wavelength, the minimum deflection angle varies with color. Lots of violet deflected at this angle Lots of red deflected at this angle Lots of light of all colors is deflected by >138°, so the region below rainbow is bright and white.

Explanation of 2nd rainbow The 2nd (upper) rainbow results from light entering the droplet in its lower half and making 2 internal reflections in the droplet. Water droplet Minimum deflection angle (~232.5°) yielding a rainbow radius of 52.5°. Because energy is lost at each reflection, the 2nd rainbow is weaker. 3rd and 4th rainbows are even weaker, are more spread out, and are toward the sun. 5th rainbow overlaps the 2nd, and 6th is below the 1st, but are too weak to see.

Coherent vs. Incoherent light scattering Coherent light scattering: scattered wavelets have nonrandom relative phases in the direction of interest. Incoherent light scattering: scattered wavelets have random relative phases in the direction of interest. Example: Forward scattering is coherent— even if the scatterers are randomly arranged in space. Path lengths are equal. Off-axis scattering is incoherent when the scatterers are randomly arranged in space. Path lengths are random.

Coherent vs. Incoherent Scattering Total complex amplitude, . Irradiance, I µ A2. So: Icoh µ N2 Incoherent scattering: Total complex amplitude, The irradiance So incoherent scattering is weaker than coherent scattering, but not zero. qm=qn

Why the sky is blue Air molecules scatter light, and the scattering is proportional to w4 Blue light is scattered out of the beam, leaving yellow light behind, so the sun appears yellow.