Part V. Optics Reflection & Refraction Images & Optical Instruments Interference & Diffraction

Drops of dew act as miniature optical systems, with light refracting through the drops to form myriad images of the background flowers －which themselves are out of focus in the photographer’s camera.

30. Reflection & Refraction Total Internal Reflection Dispersion

Why does the bee’s image appear at left, and what does this have to do with e-mail and the Internet? Ans: Total internal reflection; fibre optics.

30.1. Reflection Conductor: E of light drives e to oscillate  re-radiate  reflection Huygens-Fresnel principle : Each point of an advancing wave front is the source of new (spherical) waves. The new wave front is tangent to all these waves. angle of incidence = angle of reflection  = 

Specular reflection ( smooth surface ) Diffuse reflection ( rough surface )

Example 30.1. The Corner Reflector Two mirrors join at right angles. Show that any light ray incident in the plane of the page will return anti-parallel to its incident direction. Ray turned by angle B here Ray turned by angle A here

Partial Reflection Continuity of fields at boundary  incident waves always partly reflected. Least reflection at normal incidence (4% for glass). Anti-reflection coating for lens, solar cells…

30.2. Refraction index of refraction Wave speeds differ in different media. Observers at A & B count same number of wave crests at any given duration  wave frequency doesn’t change in crossing media.   smaller for medium with slower v or higher n.

Table 30.1. Indices of Refraction

1 1 2  Snell’s law

Example 30.2. Plane Slab A light ray propagating in air strikes a glass slab of thickness d and refractive index n at incidence angle 1. Show that it emerges from the stab propagating parallel to the original direction. At 1st (upper) interface At 2nd (lower) interface Since

Example 30.3. CD Music The laser beam that reads information from a compact disc is 0.737 mm wide when it strikes the disc, and it forms a cone with half angle 1 = 27.0. It then passes through a 1.20 mm thick layer of plastic with refractive index 1.55 before reaching the reflective information layer near the disc’s top surface. What is the beam diameter d at the information layer? At the incidence (lower) interface: At the information (upper) surface:

GOT IT? 30.1. The figure shows the path of a light ray through three different media. Rank the media according to their refractive indices. n3 > n1 > n2

Multiple & Continuous Refraction Air’s temperature-dependent refractive index results in the shimmering mirages you see on highways. What you’re actually seeing is refracted sky light.

Refraction, Reflection, & Polarization Incident beam with in-plane polarization: no reflection when refr = p  Brewster (or polarizing) angle ( reflected beam longitudinal: not EM )l p  56 for air-glass Reflected light is perpendicularly polarized if incidence is at p .

30.3. Total Internal Reflection Critical angle c for total internal reflection ( refr  90 ) n1 > n2

Example 30.4. Whale Watch Planeloads of whale watchers fly over the ocean. Within what range of viewing angles can the whale see the planes? The whale sees the entire world above the surface in a cone of half-angle θc ; beyond that, it sees reflections of objects below the surface.

GOT IT? 30.2. The glass prism in figure has n = 1.5 and is surrounded by air ( n = 1 ). What would happen the the incident light ray if the prism is imersed in water ( n = 1.333 )? Beam is both reflected & refracted at the diagonal interface .

Application: Optical Fibre Typical fibre: glass core of d = 8 m, cladded by smaller n glass. total internal reflection Typical transmission ~ km. SemiC laser:  = 850, 1350, 1550 nm Required bandwidths: Audio: kHz TV: 6 Mhz Microwave freq: 1010 Hz Light freq: 1014 Hz

30.4. Dispersion v depends on   n depends on  : dispersion Dispersion separates the colors in white light, with shorter-wavelength violet experiencing the greatest refraction.

Rainbow Double rainbow and supernumerary rainbows on the inside of the primary arc. The shadow of the photographer's head marks the centre of the rainbow circle (antisolar point).

The primary rainbow results from total reflection in raindrops that concentrates light at approximately 42° deflection. Dispersion separates wavelengths slightly, resulting in the rainbow’s colors. The rainbow is a circular arc located at 42 ° from the line that connects the Sun, the observer, and the center of the arc.

Light rays enter a raindrop from one direction (typically a straight line from the Sun), reflect off the back of the raindrop, and fan out as they leave the raindrop. The light leaving the rainbow is spread over a wide angle, with a maximum intensity at 40.89–42°. White light separates into different colours on entering the raindrop because red light is refracted by a lesser angle than blue light. On leaving the raindrop, the red rays have turned through a smaller angle than the blue rays, producing a rainbow.

Glass lenses: chromatic aberration. The spectrum of a diffuse gas－here hydrogen－consists of light at discrete wavelengths. Glass lenses: chromatic aberration. Varying ionization level in ionosphere  dispersion in radio waves Comparing travel times of radio waves of different freq reveals atmospheric conditions  dual-freq GPS with cm resolution