 Why is the sky blue?  How do rainbows work?

Refraction Of Light

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

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

 The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane  The angle of refraction, θ 2, depends on the properties of the medium

 Ray  is the incident ray  Ray  is the reflected ray  Ray is refracted into the lucite  Ray  is internally reflected in the lucite  Ray is refracted as it enters the air from the lucite

 Light is refracted because the speed of light varies in different media ◦ n air = 1.00 ◦ n glass = ◦ n diamond =  The speed of light varies in different media because of varying time lags in absorption and re-emission of light due to electronic structure

 The index of refraction, n, of a medium can be defined  For a vacuum, n = 1  For other media, n > 1  n is a unitless ratio  When n>1, light slows down to maintain frequency

Chapter 14

 Discovered experimentally n 1 sin θ 1 = n 2 sin θ 2 ◦ θ 1 is the angle of incidence  30.0° in this diagram ◦ θ 2 is the angle of refraction

 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 ◦ Red deviates the least

Fig , p.697

 The index of refraction for a material usually decreases with increasing wavelength  Violet light refracts more than red light when passing from air into a material  This phenomena is also known as dispersion

 A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane  Lenses are commonly used to form images by refraction in optical instruments

 These are examples of converging lenses  They have positive focal lengths  They are thickest in the middle

 These are examples of diverging lenses  They have negative focal lengths  They are thickest at the edges

 The focal length, ƒ, is the image distance that corresponds to an infinite object distance ◦ This is the same as for mirrors  A thin lens has two focal points, corresponding to parallel rays from the left and from the right ◦ A thin lens is one in which the distance between the surface of the lens and the center of the lens is negligible

 The parallel rays pass through the lens and converge at the focal point  The parallel rays can come from the left or right of the lens

 The parallel rays diverge after passing through the diverging lens  The focal point is the point where the rays appear to have originated

Chapter 14

 The equations can be used for both converging and diverging lenses ◦ A converging lens has a positive focal length ◦ A diverging lens has a negative focal length

 The geometric derivation of the equations is very similar to that of mirrors

Lens Type Object Beyond Focal Point ObjectAt Focal Point ObjectBetween And Lens Converging(convex) Real Inverted Reduced Image No Image Formed Erect Virtual Magnified Image Diverging(concave) Virtual Erect Reduced Image

Quantity Positive When Negative When Object location (p) Object is in front of the lens Object is in back of the lens Image location (q) Image is in back of the lens (real image) Image is in front of the lens (virtual image) Image height (h’) Image is upright Image is inverted Magnification Image is upright Image is inverted Focal length (f) Converging lens Diverging lens

 The image is real  The image is inverted

 The image is virtual  The image is upright

 The image is virtual  The image is upright

 Ray diagrams are essential for understanding the overall image formation  Three rays are drawn ◦ The first ray is drawn parallel to the first principle axis and then passes through (or appears to come from) one of the focal lengths ◦ The second ray is drawn through the center of the lens and continues in a straight line ◦ The third ray is drawn from the other focal point and emerges from the lens parallel to the principle axis  There are an infinite number of rays, these are convenient

 A ray of light strikes a drop of water in the atmosphere  It undergoes both reflection and refraction ◦ First refraction at the front of the drop  Violet light will deviate the most  Red light will deviate the least

 A prism spectrometer uses a prism to cause the wavelengths to separate  The instrument is commonly used to study wavelengths emitted by a light source

 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 When the incident angle is equal to the critical angle, total internal reflection occurs

 A particular angle of incidence will result in an angle of refraction of 90°  This angle of incidence is called the critical angle n 1 sinθ c =n 2 sin90 Therefore: sinθ c = n 2 n 1 Calculate the critical angle for a Plastic light guide, n=1.49

 An application of internal reflection  Plastic or glass rods are used to “pipe” light from one place to another  Applications include ◦ medical use of fiber optic cables for diagnosis and correction of medical problems ◦ Telecommunications  Internet ◦ Dash board lighting

Fig , p.705

 Huygen assumed that light is a form of wave motion rather than a stream of particles  Huygen’s Principle is a geometric construction for determining the position of a new wave at some point based on the knowledge of the wave front that preceded it

 All points on a given wave front are taken as point sources for the production of spherical secondary waves, called wavelets, which propagate in the forward direction with speeds characteristic of waves in that medium ◦ After some time has elapsed, the new position of the wave front is the surface tangent to the wavelets

 At t = 0, the wave front is indicated by the plane AA’  The points are representative sources for the wavelets  After the wavelets have moved a distance cΔt, a new plane BB’ can be drawn tangent to the wavefronts

 The inner arc represents part of the spherical wave  The points are representative points where wavelets are propagated  The new wavefront is tangent at each point to the wavelet

 All hot, low pressure gases emit their own characteristic spectra  The particular wavelengths emitted by a gas serve as “fingerprints” of that gas  Some uses of spectral analysis ◦ Identification of molecules ◦ Identification of elements in distant stars ◦ Identification of minerals

 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 when light enters a material depends on the wavelength of the light

 The Law of Reflection can be derived from Huygen’s Principle  AA’ is a wave front of incident light  The reflected wave front is CD

 Triangle ADC is congruent to triangle AA’C  θ 1 = θ 1 ’  This is the Law of Reflection

 In time Δt, ray 1 moves from A to B and ray 2 moves from A’ to C  From triangles AA’C and ACB, all the ratios in the Law of Refraction can be found ◦ n 1 sin θ 1 = n 2 sin θ 2

 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 bent at the boundary ◦ This bending of the ray is called refraction

 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  Total internal reflection occurs only when light attempts to move from a medium of higher index of refraction to a medium of lower index of refraction

Fig , p.694