Electromagnetic Radiation (Light): Travels in packets of energy, called Photons.

A vibrating charge, surrounded

by both an electric and a magnetic field creates electromagnetic waves. Once created the oscillating electric and magnetic
field, which are perpendicular to each other, can self sustain each other and as a result can travel through the vacuum of
empty space. We see only visible light, which is a very small portion of the entire electromagnetic spectrum. The entire
spectrum from weakest to strongest is:
Radio Waves Microwaves Infrared (IR) Visible Ultraviolet (UV) X-Rays Gamma Rays
Low energy, low frequency, long wavelength High energy, high frequency, short wavelength
Visible light follows ROY G BIV from low energy to high energy. So Blue light has higher energy than red light.
To see light, the waves must be aimed straight into our eyes to excite the photoreceptors at the back of our eyes. The colors
we see are the waves of light that reflected off of an object. The colors that are not present are the ones that passed through
the object or were absorbed by the object. Grass absorbs red and blue light needed for photosynthesis, and it reflects the
unnecessary green wavelengths.
Law of Reflection: i r
. All optical angles are measured in relation to a normal line. A normal is a line
perpendicular to the surface (Force Normal is perpendicular to the surface). When a surface is curved the normal is
perpendicular to a tangent to the curved surface. It is diagrammed as a dashed line.
Ray, smooth surface Parallel rays, smooth surface Rough surface, Diffuse reflection

i r
Fig 24.4

On a smooth surface such as a mirror the incident parallel rays of light reflect parallel, and the image formed is identical to
the object. But on a rough surface the incident parallel rays are sent in all directions and the image will be diffuse (fuzzy).
Transmitting Light: EM waves not only travel in vacuums, but that is where they are fastest. The speed of light in a
c
vacuum, c, is c 3 108 m s . The Index of refraction, n was devised as a comparison value. It compares the
v
speed of light in a medium a the known speed in a vacuum. The index of refraction for light in a vacuum is 1.00, and the
index can never be less than one. The index of refraction for air is 1.0003, which rounds to nair 1.00 .

Refraction: The bending of light as it changes mediums. The speed changes, but the frequency does not, v f so
the wavelength changes causing the path of the light to bend. Less to more, bends toward.
Less dense to more dense Light slows Frequency same Wavelength shortens Bends toward normal
More dense to less dense Light faster Frequency same Wavelength lengthens Bends away from normal

Snell’s Law: n1 sin 1 n2 sin 2 Given the speed in one or both mediums, the indices of
1
refraction or angles can be determined. With three pieces of information the fourth can be determined n1
mathematically. Fig 24.5 shows light moving from a less dense medium to a more dense medium. n1
and 1 go with the incident medium while n2 and 2 go with the refracted medium. Blue light with n2
its higher energy, higher frequency, and lower wavelength bends more than red light. It will bend more
toward the normal (less to more), and it will bend more away from the normal as well (more to less). Fig 24.5 2

Total Internal Reflection: A special case of Snell’s Law. If the incident angle is of a certain size
it will result in a 90o angle of refraction.
Less This incident angle is called the critical
dense angle . At incident angles equal to
medium 90o c

or larger than the critical angle the light

reflects back into the substance. So the
c
light at the critical angle or greater is
Fig 24.6 is larger than c. totally internally reflected. Medium 1
Rays are reflected contains the incident ray so 1 is the
critical angle and 2 is 90o. This only
works when you go from a dense to less dense medium.
n2
n1 sin c n2 sin 90o n1 sin c n2 sin c
n1

Revised 8/29/06 82 © R H Jansen

 4 25 Geometric Optics
Lenses and Mirrors: Mirrors reflect light and lenses transmit light. They both fall into two main categories.
Converging lenses and mirrors converge parallel rays of light on the focal point, and thus the focus is +f. Diverging lenses
and mirrors diverge parallel rays of light away from the focus, with a -f. The shapes, convex and concave are secondary, but
must be memorized.
Converging Lense, +f Diverging Lense, -f Converging Mirror, + f Diverging Mirror, - f
Convex Lense Concave Lense Concave Mirror Convex Mirror

Spherical Lenses and Mirrors: We are working with lenses & mirrors that have been cut from spheres. Each curved
surface has a center of curvature. The focal point is located half way between the center of curvature and the lens or mirrors
surface. Focal distance is measured from lens or mirror surface to the focal point. F r 2 and the distance to the center
is C 2F .
Ray Tracing: Remember light goes through the lens, while it bounces off mirrors.
Rules for Lenses: Rays arriving parallel to the optical axis, either converge on the far focus or diverge from the near
focus.
Rays that go through the center of the lens keep going straight.
Rules for mirrors: Rays arriving parallel to the optical axis, either converge on the near focus or diverge from the far
focus.
Rays arriving through the focus, go out parallel.
Rays that go through the center of curvature bounce (C = 2F) bounce straight back.
Images: Two types of images are formed by light interacting with lenses and mirrors. To find the location and the size of
an image use ray tracing practiced in the following worksheet. If the forward ray traces touch (converge to create an image)
the image is considered real and has a positive distance from the lens, +si. Real images can be projected on a screen. Real
images are always inverted. But, when rays diverge (separate) the forward ray traces will not intersect. You then must draw
a back ray trace through the other focus. In this case the image is virtual, and since it resulted from the intersection of the
negative ray traces it has a negative distance, si. Virtual images are always upright.
Converging Lens / Mirror: Converging Lens / Mirror: Converging Lens / Diverging lens / Mirror
Object outside of focus Object at focus Mirror: Object inside of
focus
Real Images, +si No Image: si = Virtual Image, si
Inverted, hi, and M f = so Upright, +hi, and +M

Geometric Optics
r 1 1 1
f The center of curvature is located at 2f. So the focal point is half of the radius. Shows the
2 f so si
hi si
geometric relationship between the focal length, object distance, and image distance. M Relates the
ho so
magnification to the height of the object and image, and the distance to each. The only conversions needed are in cases
where you lack unit agreement. Variables are either all the same or they cancel out. Centimeters are commonly used in
optics. The magnification formula tells the relationship between si and hi. These variables always have the opposite sign.
Remember negative M does not mean the image is smaller. It means the image is upside down. 0.5x is a smaller image
and upright, while –2.0x is a larger inverted image.
For example problems complete the Geometric Optics Worksheet.

Revised 8/29/06 83 © R H Jansen