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, θ2, 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◦ nair = 1.00◦ nglass = 1.458 -1.66◦ ndiamond = 2.419

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

v

c

mediumainlightofspeed

vacuumainlightofspeedn

Chapter 14

Chapter 14

Chapter 14

Discovered experimentally

n1 sin θ1 = n2 sin θ2 ◦ θ1 is the angle of incidence

30.0° in this diagram

◦ θ2 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. 22.16, 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

f

1

q

1

p

1

p

q

h

'hM

Lens TypeLens Type ObjectObject

Beyond Beyond Focal Focal PointPoint

Object Object

At At

Focal Focal PointPoint

ObjectObject

BetweenBetween

Focal Focal PointPoint

And LensAnd LensConvergingConverging

(convex)(convex)Real Real

Inverted Inverted Reduced Reduced ImageImage

No Image No Image FormedFormed

Erect Erect Virtual Virtual

Magnified Magnified ImageImage

DivergingDiverging

(concave)(concave)Virtual Virtual Erect Erect

Reduced Reduced ImageImage

Virtual Virtual Erect Erect

Reduced Reduced ImageImage

Virtual Virtual Erect Erect

Reduced Reduced ImageImage

QuantityQuantity Positive Positive WhenWhen

Negative Negative WhenWhen

Object location (p)Object location (p) Object is in front of Object is in front of the lensthe lens

Object is in back of Object is in back of the lensthe lens

Image location (q)Image location (q) Image is in back of Image is in back of the lens (real the lens (real image)image)

Image is in front of Image is in front of the lens (virtual the lens (virtual image)image)

Image height (h’)Image height (h’) Image is uprightImage is upright Image is invertedImage is inverted

MagnificationMagnification Image is uprightImage is upright Image is invertedImage is inverted

Focal length (f)Focal length (f) Converging lensConverging lens Diverging lensDiverging 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 When the incident angle is equal to the critical angle, total internal reflection occurscritical 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

n1sinθc=n2sin90Therefore:

sinθc= n2

n1Calculate 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. 22.29, 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

θ1 = θ1’ 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◦ n1 sin θ1 = n2 sin θ2

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. 22.12, p.694