Chapter 29 – Reflection & Refraction Chapter preview Sections Reflection The Law of Reflection Mirrors Diffuse Reflection Reflection of Sound Refraction Refraction of Sound Refraction of Light Atmospheric Refraction Dispersion in a Prism The Rainbow Total Internal Reflection

Reflection & Refraction Section 29.1—Reflection

Reflection Reflection – some or all of a wave bounces back into the first medium when hitting a boundary of a second medium When all the wave energy is reflected back instead of being transmitted, it is total reflection If some energy is transmitted and some is reflected, the wave is partially reflected

Reflection

Reflection & Refraction Section 29.2—The Law of Reflection

The Law of Reflection The direction of incidence and reflection is best described by straight-line rays Incident rays and reflected rays make equal angles with a line perpendicular to the surface, called the normal Angle of Incidence – angle made by the incident ray and the normal Angle of Reflection – angle made by the reflected ray and the normal Law of Reflection – the angle of incidence and the angle of reflection are equal

The Law of Reflection

Reflection & Refraction Section 29.3—Mirrors

Mirrors Virtual Image – the point located behind a mirror where an object appears to originate Your eye cannot tell the difference between an object and its virtual image The image is as far behind a mirror as the object is in front of the mirror

Mirrors The law of reflection holds for curved mirrors. a. The image formed by a Convex mirror is smaller than the object. b. When an object is close to a concave mirror, the image can be larger than the object. For reflections in a plane mirror, object size equals image size and object distance equals image distance.

Reflection & Refraction Section 29.4—Diffuse Reflection

Diffuse Reflection Diffuse Reflection – light incident on a rough surface is reflected in many directions A surface’s roughness is dependent upon the wavelength of the wave incident upon that surface; the longer the wavelength, the smoother the surface will appear To a piece of paper, light is reflecting diffusely The Law of Reflection is Always Observed (regardless of the orientation of the surface)

Reflection & Refraction Section 29.5—Reflection of Sound

Reflection of Sound An echo is reflected sound Sound reflects from all surfaces of a room Acoustics is the study of the way sound reflects off of objects in a room Reverberations – Multiple reflections of sound within a room The walls of concert halls are designed to make the reflection of sound diffuse

Reflection of Sound

Reflection & Refraction Section 29.6—Refraction

Refraction Refraction – the change in direction of a wave as it crosses the boundary between two media in which the wave travels at different speeds Wave Fronts – lines that represent the position of different crests At each point along a wave front, the wave is moving perpendicular to the wave front The direction of motion is best represented by a ray

Refraction Less Rigid Medium More Rigid Incident Ray Refracted Ray Less Rigid Medium _________________ More Rigid Refracted ray bends toward the normal

Refraction When one medium ends and another begins, that is called a boundary. When a wave encounters a boundary that is more dense, part of it is reflected and part of it is transmitted. The frequency of the wave is not altered when crossing a barrier, but the speed and wavelength are. The change in speed and wavelength can cause the wave to bend, if it hits the boundary at an angle other than 90°.

Reflection & Refraction Section 29.7—Refraction of Sound

Refraction of Sound Sound waves are refracted when parts of a wave front travel at different speeds This happens in uneven winds or temperatures Sound waves tend to bend away from warm ground, since it travels faster in warmer air On a cold night, the speed of sound is slower near the ground than above, so we can hear over larger distances

Refraction of Sound

Reflection & Refraction Section 29.8—Refraction of Light

Index of Refraction of a few substances Refraction of Light A pond or swimming pool may appear shallower than they actually are, a pencil in a glass of water will appear bent All of these effects are caused by changes in the speed of light as it passes from one medium to another, or through varying temperatures and densities of the same medium – which changes the directions of light rays Index of Refraction (n) = (speed of light in vacuum)/(speed of light in material) Snell’s Law: n sin θ = n´ sin θ´ (where n and n´ are the indices of refraction of the media on either side of the boundary, and θ and θ´ are the respective angles of incidence and refraction) Index of Refraction of a few substances Vacuum 1.00 Crown glass 1.52 Air 1.0003 Quartz 1.52 Water 1.33 Diamond 2.42 Ethanol 1.36

Refraction of Light Incident Ray Refracted Ray The submerged object's apparent depth equals its true depth divided by the liquid's index of refraction: d' = d(n2/n1). Note: n2 is the index of refraction of the medium above the surface and n1 is the index of refraction of the medium below the surface. Incident Ray Refracted Ray

Refraction of Light Figure 29.19 There are many effects of refraction a. The apparent depth of the glass block is less than the real depth. b. The fish appears to be nearer than it actually is. c. The full glass mug appears to hold more root beer than it actually does.

Reflection & Refraction Section 29.9—Atmospheric Refraction

Atmospheric Refraction On hot days there may be a layer of very hot air in contact with the ground, the light will travel faster through this air and will bend, creating a mirage

Atmospheric Refraction When you watch the sun set, you can still see the sun for several minutes after it has sunk below the horizon, because light is refracted by Earth’s atmosphere

Reflection & Refraction Section 29.10—Dispersion in a Prism

Dispersion in a Prism Light of frequencies closer to the natural frequency of the electron oscillators in a medium travels more slowly in the medium Since different frequencies of light travel at different speeds in transparent materials, they will refract differently and bend at different angles When light is bent twice at nonparallel boundaries, as in a prism, the seperation of the different colors is apparent Dispersion – the separation of light into colors arranged according to their frequency

Dispersion in a Prism

Reflection & Refraction Section 29.11—The Rainbow

The Rainbow The rainbow takes the concept of dispersion and multiples it through the atmosphere The sun shines on water droplets in a cloud or when it is raining The light is dispersed by the raindrop into its spectral colors

The Rainbow Dispersion by a Raindrop: Each droplet acts like a prism •Higher drops – red is bent to the eye •Lower drops – violet is bent to the eye

The Rainbow Rainbows will always appear at an angle between 40ᵒ and 42ᵒ . If you are lucky enough to see two rainbows at the same time, the second (much dimmer) one occurs above the main one, and results from sunlight creating a double reflection in the water droplets. The colors are also upside down.

Reflection & Refraction Section 29.12—Total Internal Reflection.

Total Internal Reflection Critical Angle: Figure 29.32 You can observe total internal reflection in your bathtub. a-d) Light emitted in the water at angles below the critical angle is partly refracted and partly reflected at the surface. e) At the critical angle, the emerging beam shims the surface. f) Past the critical angle, there is total internal reflection.

Total Internal Reflection Total Internal Reflection in Diamonds The critical angle for a diamond is 24.6ᵒ, smaller than in other common substances. This small critical angle means that light inside is more likely to totally internally reflect.

Total Internal Reflection Critical Angle – the minimum angle of incidence for which a light ray is totally reflected within a medium Total Internal Reflection – the 100% reflection of light that strikes the boundary between two media at an angle greater than the critical angle Optical fibers utilize the concept of total internal reflection to feed light from one location to another, these cables are very useful for communications

Total Internal Reflection Optical Fibers: At each contact w/ the glass air interface, if the light hits at greater than the critical angle, it undergoes total internal reflection and stays in the fiber.