Part V. Optics

30. Reflection & Refraction

31. Images & Optical Instruments

32. 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

1. Reflection

2. Refraction

3. Total Internal Reflection

4. 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 A here

Ray turned by angle B here

180A B

2A

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

Wave speeds differ in different media.c

nv

index of refraction

v c

f n f smaller for medium with slower v or higher n.

Observers at A & B count same number of wave crests at any given duration

wave frequency doesn’t change in crossing media.

Table 30.1. Indices of Refraction

1 1

2

1 1

1 1 2 2sin sinn n Snell’s law

1 2

1 2sin sin

v t v t

cv

n

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 1 2sin sinn

At 2nd (lower) interface 3 4sin sinn

3 2 Since

1 4

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:

1 2sin sinn

2d D x 22 tanD t

At the information (upper) surface:

1 sin 27.00.737 2 1.2 tan sin

1.55mm mm

0.00180mm 1.80 m

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

90refr p

( reflected beam longitudinal: not EM )l

1 2sin sinp refrn n 2 sin 90 pn 2 cos pn

2

1

tan p

n

n 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 )

1 2sin cn n n1 > n2

Example 30.4. Whale Watch

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.

Planeloads of whale watchers fly over the ocean.

Within what range of viewing angles can the whale see the planes?

1sin

1.333c

48.6c

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: kHzTV: 6 Mhz

Microwave freq: 1010 Hz Light freq: 1014 Hz

30.4. Dispersion

Dispersion separates the colors in white light, with shorter-wavelength violet experiencing the greatest refraction.

v depends on n depends on : dispersion

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.

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