1

Reflection and Refraction

incident beam reflected beam

refracted beam

GLASS

In general, light that is incident on an interface will be partially reflected and partially refracted.

2

In order to avoid clutter from drawing wavefronts, the propogationof light can be visualized by drawing rays instead.

A ray is a line drawn in space along the direction of flow of radiant energy. If the medium is isotropic (behaves the same in every direction), the rays are perpendicular to the wavefronts.

Point source

Spherical wavefronts

Rays

Planar wavefronts

Rays

Rays:

(b) For planar waves, the rays are all parallel. (Also, rather than sketching bundles of rays, we can select one ray to represent the beam of plane waves.)

(a) For a point source emitting spherical waves, the rays point radially outward from the source.

Examples:

(a) (b)

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Reflection

Reflection occurs at the surface between two materials with different 𝑛.

𝑛𝑖 < 𝑛𝑡

𝑛𝑖 > 𝑛𝑡

Reflection can be categorized as “external” or “internal” depending on the relative values of 𝑛 of the two materials:

External reflection

Internal reflection

Aire.g

Air

Water

Watere.g

𝑛 = 1

𝑛 = 1

𝑛 = 1.3

𝑛 = 1.3

incident medium has a smallerrefractive index than the transmitted medium.

incident medium has a largerrefractive index than the transmitted medium.

4

1. The angle-of-incidence equals the angle-of-reflection

𝜃𝑖 = 𝜃𝑟

The figure only shows one representative incident ray and one representative reflected ray.

Law of Reflection:

All angles in the relevant formulae are measured from the perpendicular (or normal)to the surface.

2. The incident ray, the normal to the surface, and the reflected ray all lie in a plane. The plane is called the plane-of-incidence.

The Law of Reflection

𝜃𝑖 is the angle of incidence

𝜃𝑟 is the angle of reflection

Note: Law of reflection is reversible.

(Arrows on the rays can be reversed and the resulting picture is still true.)

[see end of this handout for derivation of "𝜃𝑖 = 𝜃𝑟"]

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Specular vs Diffuse Reflection

Smooth surface: Rough surface:

specular reflection diffuse reflection

“smooth” surface = peaks and valleys on the surface are small compared to 𝜆

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Example: Stealth technology (pictures from Wikipedia)

Flat tilted-planes:

- scatter the microwaves away from their source.

F-117A Stealth fighter

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Derivation of the 1st part of the Law of Reflection

𝜽𝒊 = 𝜽𝒓

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Reflection: Microscopic description

When an incident plane wavefrontstrikes the surface at some angle, it does not reach all the atoms along the surface at the same time.

Each affected atom emits a hemi-spherical wave back into the incident medium.

The wavelets emitted back into the incident medium advance together and add constructively in only one direction: there is one well-defined reflected beam.

Assume a beam composed of plane wavefronts impinge at some angle on a smooth, flat surface of a dense medium (wavelength of light is many times the atom size/spacing).

9

Reflection: Geometry of Constructive Interference

Line 𝐴𝐵 lies along an incoming plane wave wavefront, while 𝐶𝐷 lies on an outgoing wavefront. The phases at A and B are the same. The phases at C and D are the same.

Consider two atoms A and D on the surface

The wavelet emitted from A will arrive at C in-phase with the waveletjust being emitted from D (as it is stimulated by B) as long as thedistances 𝐴𝐶 and 𝐵𝐷 are equal. i.e., 𝐴𝐶 = 𝐵𝐷

The right-angle triangles ABD and ACD share a common hypotenuse 𝐴𝐷, and so

𝐴𝐷sin𝜃𝑖 = 𝐵𝐷 𝐴𝐷sin𝜃𝑟 = 𝐴𝐶and

Hence, sin𝜃𝑖 = sin𝜃𝑟 or 𝜃𝑖 = 𝜃𝑟

The Law of Reflection (1st part):The angle-of-incidence equals the angle-of-reflection

𝜃𝑖 = 𝜃𝑟