Optics
The field of geometrical optics refers to light behavior that can be explained using straight lines
or _________ of light. This field of study can be used to explain the formation of any image.
Law of Reflection: Angle of Incidence = Angle of Reflection
See problems in packet one.
Two types of reflection:
Diffuse reflection- parallel rays of light hit an object and spread out in all directions.
This type of reflection is typically associated with rough / smooth (Circle One)surfaces.
_________ reflection- parallel rays strike an object and reflect off still parallel to each
other. This type of reflection is typically associated with rough / smooth (Circle One)surfaces.
How do you see objects: you see objects only when light is _________ from them and enters the
eye. Consequently every object we see exhibits at least some diffuse reflection.
The index of refraction
The index of refraction is measure of the optical density of a material. As the index of refraction
increases a material is considered to be more ____________ ____________. Below is the
formula for the index of refraction.
n = the index of refraction of a particular substance
c = the speed of light
vs = the speed of light through that substance
The lowest possible value for the index of refraction is ____________. This is because nothing
can exceed the speed of __________.
The index of refraction for crown glass equals 1.52 . Determine the speed of light in crown
glass.
Refraction
Refraction is the bending that occurs when a wave(remember light is a wave as well as a
particle) passes into a new __________ medium where it travels at a different __________. If a
wave enters a new medium head-on even if the speed changes it will not __________.
If a wave speeds up when entering the new material it will bend toward/away (Circle One) from
the perpendicular.
If a wave slows down when entering the new material it will bend toward/away (Circle One)
from the perpendicular.
Snell’s Law
ni sini = nr sinr
where nI= the index of refraction in the material that the light wave starts in.
I= the angle of incidence, this is the angle between the incident ray and the
_______________
nr= the index of refraction of the material that the wave is going _________.
r= the angle of refraction, this is the angle between the refracted ray in the new material
and the ________________
Draw a picture of a ray going from a material of greater optical density (higher index of
refraction) into a material of lesser optical density (lower index of refraction)
When a ray of light goes from a higher index of refraction to a lower index of refraction it bends
towards / away from (Circle One) the perpendicular. The reverse holds true as well.
Refraction problems:
A ray of light goes from lucite (n=1.51) into water (n=1.33) at angle of 30 degrees measured
from the perpendicular. Determine the angle at which the light enters the water.
A diver shines a flashlight upward from beneath the water at an angle of 60 degrees with the
surface of the water. At what angle does the beam leave the water?
Total Internal Reflection
When light passes into a material of lower optical density light bends away from the
_____________. If the angle of incidence is great enough the light will not be able to escape
into the material of lower optical density. When this happens ___________ __________
___________ occurs. This can only happen when light travels from a material of greater optical
density to a material of ___________ optical density.
The smallest angle at which total internal reflection occurs is the ____________ angle. If the
angle of incidence is equal to or greater than this value the light will not escape. Instead it
bounce of the boundary between the two mediums and obey the __________ __________
_____________.
The formula relating the critical angle with the indicies of refraction for the two medium is given
below.
Where c is the critical angle.
n1 is the index of refraction of the material in which the light begins
n2 is the index of refraction of the material the light is trying to enter, but can not (n1> n2)
Total Internal Refraction has many important applications because it allows light to be bent or be
send long distances without loss of intensity. It is used in many optical instruments in place of
mirrors and in fiber optic cables.
Problems
Calculate the critical angel of light going from water into air.
Is total internal reflection possible going from air into water?
The critical angle for a certain liquid / air surface is 42.8 degrees. Find the index of refraction
for the liquid. What is the speed that light travels through that liquid?
Image formation by a plane or __________ mirror
If you are standing in front of the mirror you are the _____________ . The distance between you
and the mirror is known as the _____________ _______________. The image is formed in
front of / behind (Circle One) a plane mirror. The distance between the mirror and the image is
known as the _____________ _____________.
Images that are located behind a mirror are known as _____________ images. These images can
/ can not (Circle One) be projected on a screen. On the other hand, ______________
_______________ can/ can not (Circle One) be projected on a screen and are located in front of /
behind (Circle One) a mirror.
The height of the image formed by a plane mirror is independent of / dependent on (Circle One)
the object distance.
When images are formed by a plane mirror, the image distance and object distance are always
_____________.
Problems:
If you are standing 2 m in front of a plane mirror where is the image located?
If you standing 1.5 m in front of a mirror taking a picture of yourself, at distance should the
camera be focused?
Yogi Bear is looking at a picnicker’s sandwich in a plane mirror. If Yogi moves twice as close to
the mirror, does he see a bigger meal? Explain using optics termonology.
What is the smallest mirror that will allow you to see all of your body at the same time?
Curved Mirrors:
A __________ mirror is sunken in. It is used for
This type of mirror is known for forming upside down or _____________ images. However
when objects are located inside the focal length the image is erect and larger.
The center of curvature is located in front of a __________ mirror. The ___________ or the
point at which parallel rays of light converge is located half way between the _____________
____ _______________ and the center of the mirror.
A __________ mirror bulges out. It often used for
Because it is formed on the outside of a sphere, its center of curvature is located ___________
the surface of the mirror. The ___________ _____________ is located half way between the
surface of the mirror and the center of curvature.
A convex mirror causes parallel rays of light to ___________________________________.
Rules for locating images formed by mirrors using ray diagrams
1. All rays start from the same point on the object.
2. Ray 1 is drawn from the object parallel to the axis and passes through the focal point after
reflection.
3. Ray 2 is drawn from the object through the focal point and is drawn parallel to the axis after
reflecting off the mirror.
4. Ray 3 connects the center of curvature and the object. Because this ray passes through the
center of curvature it will be perpendicular to the surface of the mirror and will reflect back
onto itself.
5. The image is formed where the rays intersect.
6. If the rays never intersect on the front side of the mirror, a virtual image is formed behind the
mirror.
7. To locate the virtual image, extend the rays behind the mirror using dashed lines. The image
is formed where the lines connect.
For each ray diagram determine the following:
 Is the image real or virtual?
 Is the image the same size, larger, or smaller than the original image?
 Is the image erect or inverted?
Concave Mirrors
Case 1: An object located at infinity (All light rays coming from the object are parallel.)
Case 2: An object located beyond the center of curvature.
Case 3: An object located at the center of curvature.
Case 4: An object located between the center of curvature and the focal point.
Case 5: An object at the focal point.
Case 6: An object between the focal point and the mirror.
Convex Mirrors
Convex mirrors always form the same type of image regardless of the object distance.
Using Mathematics to locate images formed by mirrors
Formulas
Things to remember:
f is ______________ for convex mirrors
When the image is ____________ or formed behind the mirror dI is _______________.
The height of the image, hi is negative if the image is _____________.
Magnification and what it means:
M> 1 the image is _____________
M< 1 the image is _____________
If M is negative the image is _____________
Problems
An object 3.0mm high is 10.0 cm in front of a concave mirror having a 12 cm radius of
curvature.
a) Find the location of the image using the mirror equation.
b) Find the magnification of the mirror.
c) What is the height of the image?
A 4.0 cm high candle is placed 10 cm in from a concave mirror having a focal length of 16 cm.
a) Where is the image located?
b) What is the height of the candle’s image?
Image formation by lenses
A ____________ lens is thicker in the middle than it is at the edges. When parallel rays of light
pass through this lens, they pass through a point behind the lens known as the ___________.
Becauss this lens concentrates the parallel beams of light to a single point this lens is sometimes
called a _______________ lens. In most cases this lens will form images on the
__________side of the lens as compared to the original object. Images that are formed on the
opposite side of a lens are known as ____________ images. This lens forms images with the
same characteristics as a ____________ mirror. The focal length of this lens is ____________.
A ____________ lens is thinner in the middle than at its edges. When parallel rays of light pass
through this lens, they _______________________ for this reason this lens is also known as a
_______________ lens. Images formed by this lens will always be ____________ regardless of
the original object’s location. The focal length of this lens is _______________.
Problems:
An object 2.5 mm high is 8.5cm to the left of a convex lens with a 5.5 cm focal length. Find the
image location and height.
A stamp collector wants to magnify images by 4.0 when the object is 3.5 cm from the lens. What
focal length lens is needed?
Aberration
Chromatic Aberration is the distortion of an image caused by differential refraction of the colors
of light through a __________.
Spherical Aberration is the distortion of an image formed by a ___________ mirror. It occurs
because a spherical mirror does not have a true ___________.