Figure 26-1Wave Fronts and Rays

Figure 26-2Spherical and Planar Wave Fronts

Figure 26-3Reflection from a Smooth Surface

Reflection

• Law of reflection

qi=qr

Figure 26-4Reflection from Smooth and Rough Surfaces

Figure 26-6Locating a Mirror Image

Figure 26-8Spherical Mirrors

Figure 26-9Concave and Convex Mirrors

Figure 26-10Parallel Rays on a Convex Mirror

Figure 26-12Parallel Rays on a Concave Mirror

Figure 26-13Spherical Aberration and the Parabolic Mirror

Figure 26-14Principal Rays Used in Ray Tracing for a Concave Mirror

Figure 26-15Principal Rays Used in Ray Tracing for a Convex Mirror

Figure 26-17Image Size and Location in a

Convex Mirror

Figure 26-18Image Formation with a Concave Mirror

Example 26-3Image Formation

Mirrors

The mirror equation

0

1 1 1

id d f

Mirrors

Magnification

i i

o o

h dm

h d

Mirrors

do =distance of the object from the mirrordi =distance of the image from the mirrorf= focal length of the mirror

Mirrors

Distances in front of the mirror are positive.Distances behind the mirror are negative.

Table 26-1Imaging Characteristics of Convex

and Concave Spherical Mirrors

Convex Mirror

Object location Image orientation Image size Image type

Arbitrary Upright Reduced Virtual

Concave Mirror

Object location Image orientation Image size Image type

Beyond C Inverted Reduced Real

C Inverted Same as object Real

Between F and C Inverted Enlarged Real

Just beyond F Inverted Approaching infinity Real

Just inside F Upright Approaching infinity Virtual

Between mirror and F Upright Enlarged Virtual

Mirrors

Mirror problems:19, and 21-24 on page 883.Ray tracing worksheet.

Refraction

When light transitions between two media with different indices of refraction, it will change direction if it transitions at an angle to the demarcation between the two media.

Refraction

Angles of incidence and angles of refraction are measured in reference to a line normal (perpendicular) to the line of demarcation between media.

The index of refraction (n) for a medium is defined as the speed of light in vacuum (c) divided by the speed of light in the medium(v).

cn

v

Exercise 26-4Find the angle of refraction

Refraction

There is a mathematical relationship that is used to calculate the amount of bending called Snell’s Law.

Refraction

1 1 2 2sin sinn n

Refraction

If a ray is transitioning from a medium of lesser n to a medium of greater n it will bend toward the normal.

Refraction

If a ray is transitioning from a medium of greater n to a medium of lesser n it will bend away from the normal.

Figure 26-24Light Propagating Through a Glass Slab

Refraction

Problems 37-42 on page 883.

Lenses

Refractive properties of materials are useful in manipulating light for imaging purposes through the use of lenses.

Lenses

Lenses consist of two main types converging and diverging.

Figure 26-29A Variety of Converging and Diverging Lenses

Figure 26-32The Three Principal Rays

Used for Ray Tracing with Convex Lenses

Figure 26-33The Three Principal Rays

Used for Ray Tracing with Concave Lenses

Figure 26-35aRay Tracing for a Convex Lens

Figure 26-34The Image Formed by a Concave Lens

Lenses

The lens equation

0

1 1 1

id d f

Lenses

Magnification

i i

o o

h dm

h d

Lenses

do =distance of the object from the lensdi =distance of the image from the lensf= focal length of the lens

LensesFocal lengthf is positive for converging(convex) lenses f is negative for diverging (concave) lensesMagnificationm is positive for upright images (same orientation as the object) m is negative for inverted images (opposite orientation of object)

LensesImage distancedi is positive for real images (on the opposite side of the lens from the object)di is negative for virtual images (on the same side of the lens from the object)Magnificationm is positive for upright images (same orientation as the object) m is negative for inverted images (opposite orientation of object)

Lensesdo is positive for real objects (from which light diverges)do is negative for virtual objects (toward which light converges)

Lenses

Problems 63-67 on page 885.Ray tracing worksheet.

Dispersion of light

The index of refraction in a substance is different for light of different frequencies.

Dispersion of light

The greater the frequency, the greater the index of refraction.

Dispersion of light

Violet light will bend more than red light or green light, and therefore a separation of colors occurs.

Example 26-8Prismatics

Figure 26-37Dispersion in a Raindrop

Figure 26-38How Rainbows Are Produced

Dispersion of light

Problem 77 on p 885