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Optics
- Reflection
- Diffuse reflection
- Refraction
- Index of refraction
- Speed of light
- Snell’s law
- Geometry problems
- Critical angle
- Total internal reflection
- Brewster angle
- Fiber optics
- Mirages
- Dispersion
- Prisms
- Rainbows
- Plane mirrors
- Spherical aberration
- Concave and convex mirrors
- Focal length & radius of curvature
- Mirror / lens equation
- Convex and concave lenses
- Human eye
- Chromatic aberration
- Telescopes
- Huygens’ principle
- Diffraction Docsity.com
Reflection
Most things we see are thanks to reflections, since most objects don’t produce their own visible light. Much of the light incident on an object is absorbed but some is reflected. the wavelengths of the reflected light determine the colors we see. When white light hits an apple, for instance, primarily red wavelengths are reflected, while much of the others are absorbed.
A ray of light heading towards an object is called an incident ray. If it reflects off the object, it is called a reflected ray. A perpendicular line drawn at any point on a surface is called a normal (just like with normal force). The angle between the incident ray and normal is called the angle of incidence, i , and the angle between the reflected ray and the normal ray is called the angle of reflection, r****. The law of reflection states that the angle of incidence is always equal to the angle of reflection.
Diffuse Reflection
Diffuse reflection is when light bounces off a non-smooth surface. Each ray of light still obeys the law of reflection, but because the surface is not smooth, the normal can point in a different for every ray. If many light rays strike a non-smooth surface, they could be reflected in many different directions. This explains how we can see objects even when it seems the light shining upon it should not reflect in the direction of our eyes. It also helps to explain glare on wet roads: Water fills in and smoothes out the rough road surface so that the road becomes more like a mirror.
Speed of Light & Refraction
As you have already learned, light is extremely fast, about 3 108 m/s in a vacuum. Light, however, is slowed down by the presence of matter. The extent to which this occurs depends on what the light is traveling through. Light travels at about 3/4 of its vacuum speed (0.75 c ) in water and about 2/3 its vacuum speed (0.67 c ) in glass. The reason for this slowing is because when light strikes an atom it must interact with its electron cloud. If light travels from one medium to another, and if the speeds in these media differ, then light is subject to refraction (a changing of direction at the interface).
Refraction of light waves
Refraction of light rays
Axle Analogy
r
Imagine you’re on a skateboard heading from the sidewalk toward some grass at an angle. Your front axle is depicted before and after entering the grass. Your right contacts the grass first and slows, but your left wheel is still moving quickly on the sidewalk. This causes a turn toward the normal. If you skated from grass to sidewalk, the same path would be followed. In this case your right wheel would reach the sidewalk first and speed up, but your left wheel would still be moving more slowly. The result this time would be turning away from the normal. Skating from sidewalk to grass is like light traveling from air to a more
grass
sidewalk
overhead view “optically dense” medium like glass or water. The slower light travels in the new medium, the more it bends toward the normal. Light traveling from water to air speeds up and bends away from the normal. As with a skateboard, light traveling along the normal will change speed but not direction. Docsity.com
Index of Refraction, n
The index of refraction of a substance is the ratio of the speed in light in a vacuum to the speed of light in that substance:
n = Index of Refraction
c = Speed of light in vacuum
v = Speed of light in medium
n =
c
v
Note that a large index of refraction corresponds to a relatively slow light speed in that medium.
Medium
Vacuum
Air (STP)
Water (20º C)
Ethanol
Glass
Diamond
n
2.42Docsity.com
Snell’s Law Derivation (^) Two parallel rays are shown.
Points A and B are directly opposite one another. The top pair is at one point in time, and the bottom pair after time t. The dashed lines connecting the pairs are perpendicular to the rays. In time t , point A travels a distance x, while point B travels a distance y. sin 1 = x / d, so x = d sin (^1)
sin 2 = y / d, so y = d sin (^2) Speed of A: v 1 = x / t Speed of B: v 2 = y / t Continued…
-^ •
A
A B
B
1
2
x
y
d
n 1
n 2
Docsity.com
Snell’s Law Derivation
(cont.)
v 1 / c sin 1 1 / n 1 sin 1 n 2 v 2 / c sin 2 1 / n 2 sin (^) 2 n 1
= =^ =
n 1 sin 1 = n 2 sin (^2)
v 1 x / t x sin (^1)
v 2 y / t y sin (^2)
= = So,
-^ •
A
A B
B
1
2
x
y
d
n 1
n 2
Refraction Problem
d
glass
H 20
H 20
10m
0.504 m
5.2 · 10 -8^ s
n 1 = 1.
n 2 = 1.
Goal: Find the distance the light ray displaced due to the thick window and how much time it spends in the glass. Some hints are given.
- Find 1 (just for fun).
- To show incoming & outgoing rays are parallel, find_._
- Find d.
- Find the time the light spends in the glass. Extra practice: Find if bottom medium is replaced with air.
Refraction Problem
Goal: Find the exit angle relative to the horizontal.
glass
air
The triangle is isosceles. Incident ray is horizontal, parallel to the base.
The Brewster angle is the angle of incidence the produces reflected and refracted rays that are perpendicular.
Brewster Angle
From Snell, n 1 sin b = n 2 sin.
α = b since + = 90º,
and b + = 90º.
β = since + = 90º,
and + = 90º. Thus,
n 1 sin b = n 2 sin = n 2 sin = n 2 cos b
tan b = n 2 / n 1
b b
n 2
n 1
Sir David Brewster
Critical Angle
The incident angle that causes the refracted ray to skim right along the boundary of a substance is known as the critical angle, (^) c. The critical angle is the angle of incidence that produces an angle of refraction of 90º. If the angle of incidence exceeds the critical angle, the ray is completely reflected and does not enter the new medium. A critical angle only exists when light is attempting to penetrate a medium of higher optical density than it is currently traveling in.
c =^ sin
-1 n r
n i
n i
n r
c
From Snell,
n 1 sin c = n 2 sin 90
Since sin 90 = 1, we
have n 1 sin c = n 2 and
the critical angle is
Total Internal Reflection
Total internal reflection occurs when light attempts to pass from a more optically dense medium to a less optically dense medium at an angle greater than the critical angle. When this occurs there is no refraction, only reflection.
n 1
n 2
Total internal reflection can be used for practical applications like fiber optics.
> c
n 2 > n 1
Fiber Optics
Fiber optic lines are strands of glass or transparent fibers that allows the transmission of light and digital information over long distances. They are used for the telephone system, the cable TV system, the internet, medical imaging, and mechanical engineering inspection.
Optical fibers have many advantages over copper wires. They are less expensive, thinner, lightweight, and more flexible. They aren’t flammable since they use light signals instead of electric signals. Light signals from one fiber do not interfere with signals in nearby fibers, which means clearer TV reception or phone conversations.
A fiber optic wire
spool of optical fiber
Continued… Docsity.com
