Reflection and Refraction Chapter 30 Reflection and Refraction

Geometric Optics and Ray Approximation Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media The ray approximation is used to represent beams of light – a ray of light is an imaginary line drawn along the direction of travel of the light beams A wave front is a surface passing through points of a wave that have the same phase The rays, corresponding to the direction of the wave motion, are perpendicular to the wave front

Geometric Optics and Ray Approximation Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media The ray approximation is used to represent beams of light – a ray of light is an imaginary line drawn along the direction of travel of the light beams A wave front is a surface passing through points of a wave that have the same phase The rays, corresponding to the direction of the wave motion, are perpendicular to the wave front

Specular Reflection Specular reflection is reflection from a smooth surface The reflected rays are parallel to each other All reflection in this chapter is assumed to be specular

Diffuse Reflection Diffuse reflection is reflection from a rough surface The reflected rays travel in a variety of directions Diffuse reflection makes the dry road easy to see at night

Law of Reflection The normal is a line perpendicular to the surface at the point where the incident ray strikes the surface The incident ray makes an angle of θ1 with the normal and the reflected ray makes an angle of θ1’ with the normal The angle of reflection is equal to the angle of incidence: θ1= θ1’

Refraction of Light When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium The ray that enters the second medium is refracted – bent at the boundary

Refraction of Light The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane The angle of refraction, θ2, depends on the properties of the medium and the angle of incidence The path of the light through the refracting surface is reversible

Refraction of Light Ray  is the incident ray Ray  is the reflected ray Ray  is refracted into the crystal Ray  is internally reflected in the crystal Ray  is refracted as it enters the air from the crystal

Refraction of Light Light may refract into a material where its speed is lower The angle of refraction is less than the angle of incidence so the ray bends toward the normal

Refraction of Light Light may refract into a material where its speed is higher The angle of refraction is greater than the angle of incidence so the ray bends away from the normal

The Index of Refraction When light passes from one medium to another, it is refracted because the speed of light is different in the two media The index of refraction, n, of a medium can be defined n is a unitless ratio For a vacuum, n = 1 whereas for other media, n > 1

The Index of Refraction The wavefronts do not pile up, nor are created or destroyed at the boundary Therefore, as light travels from one medium to another, its frequency does not change Both the wave speed and the wavelength do change

The Index of Refraction v1 = ƒ λ1 v2 = ƒ λ2 The ratio of the indices of refraction of the two media can be expressed as various ratios

Snell’s Law of Refraction Willebrord Snel van Royen 1580 – 1626 Snell’s Law of Refraction n1 sin θ1 = n2 sin θ2

Chapter 30 Problem 35 You’re standing 2.3 m horizontally from the edge of a 4.5-m-deep lake, with your eyes 1.7 m above the water’s surface. A diver holding a flashlight at the lake bottom shines the light so you can see it. If the light in the water makes a 42° angle with the vertical, at what horizontal distance is the diver from the edge of the lake?

Atmospheric Refraction There are many interesting results of refraction in the atmosphere At sunsets, light rays from the sun are bent as they pass into the atmosphere It is a gradual bend because the light passes through layers of the atmosphere, and each layer has a slightly different index of refraction The Sun is seen to be above the horizon even after it has fallen below

Atmospheric Refraction A mirage can be observed when the air above the ground is warmer than the air at higher elevations The rays in path B are directed toward the ground and then bent by refraction The observer sees both an upright and an inverted image

Atmospheric Refraction

Polarization by Reflection When an unpolarized light beam is reflected from a surface, the reflected light can be completely polarized, partially polarized, or unpolarized It depends on the angle of incidence If the angle is 0° or 90°, the reflected beam is unpolarized For angles between this, there is some degree of polarization For one particular angle, the beam is completely polarized

Polarization by Reflection The angle of incidence for which the reflected beam is completely polarized is called the polarizing (or Brewster’s) angle, θp Brewster’s Law relates the polarizing angle to the index of refraction for the material Sir David Brewster 1781 – 1868

Total Internal Reflection Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction Ray 5 shows internal reflection

Critical Angle A particular angle of incidence (critical angle) will result in an angle of refraction of 90° For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary This ray obeys the Law of Reflection at the boundary

Chapter 30 Problem 48 Find a simple expression for the speed of light in a material in terms of c and the critical angle at an interface between the material and vacuum.

Fiber Optics Utilizes internal reflection Plastic or glass rods are used to “pipe” light from one place to another Applications include diagnosis and correction of medical problems, telecommunications, etc.

Dispersion The index of refraction in anything except a vacuum depends on the wavelength of the light This dependence of n on λ is called dispersion Snell’s Law indicates that the angle of refraction made when light enters a material depends on the wavelength of the light The index of refraction for a material usually decreases with increasing wavelength

Refraction in a Prism The amount the ray is bent away from its original direction is called the angle of deviation, δ Since all the colors have different angles of deviation, they will spread out into a spectrum: violet deviates the most and red deviates the least

Spectroscopy A prism spectrometer uses a prism to cause the wavelengths to separate (to study wavelengths emitted by a light source) All hot, low pressure gases emit their own characteristic spectra with the particular wavelengths emitted by a gas serving as “fingerprints” of that gas Spectral analysis: identification of molecules, minerals, elements in distant stars, etc.

The Rainbow A ray of light strikes a drop of water in the atmosphere and undergoes both reflection and refraction First refraction at the front of the drop: violet light will deviate the most and red – the least At the back surface the light is reflected and refracted again as it returns to the front surface and moves into the air The rays leave the drop at various angles

The Rainbow If a raindrop high in the sky is observed, the red ray is seen A drop lower in the sky would direct violet light to the observer The other colors of the spectra lie in between the red and the violet

Answers to Even Numbered Problems Chapter 30: Problem 12 4

Answers to Even Numbered Problems Chapter 30: Problem 36 1.3 m

Answers to Even Numbered Problems Chapter 30: Problem 38 42°