When we talk about critical angles, we are talking about something called Total Internal Reflection (TIR). What is TIR? Well, if a wave enters a fast medium at a certain angle of incidence, the angle of refraction will be greater than or equal to 90 degrees. It will no longer be headed away from the boundary. Take a look at the diagram below.

Do you see? The angle of refraction is too great. The Critical Angle is the largest angle of incidence that we can have before the refracted wave is greater than or equal to 90 degrees. If the angle of incidence is greater than the critical angle- we have total internal reflection. The best way to explain TIR is to illustrate it.

If the Angle of Incidence is larger than the Critical Angle, the Angle of Refraction will be greater than 90° therefore the light reflects off the boundary. This is called Total Internal Reflection.

These two conditions must be met for TIR to happen:

The light wave is passing from a slow medium to a fast one. Therefore, n2 < n1
The Angle of Incidence will be greater than the critical angle. The critical angle marking the spot in which total internal reflection will occur if the angle of incidence is greater than it. Every material has its critical angle.

To find the Critical Angle, we manipulate Snell's Law.

n1 * sin 1 = n2 * sin 2 <------ We can say that sin 2 = 90°, which in turn equals 1.
sin 1 = n2/n1 <------- sin 1 when found will be the critical angle, so the formula will look like:

sin c = n2/n1

Click on this logo to see how Total Internal Reflection works. Be sure to "shine the light" near to the edges of the applet window.

Only part of physics deals with memorizing the infinite number of formulas that could be used. That sounds fun though, doesn't it? It also is very important to understand the relevance of what you are studying. For example, what are the advantages of Total Internal Reflection?

The biggest advantage is that all of the light is reflected. Is this like a mirror? No. A mirror only reflects about 90%, the other 10% gets absorbed by the mirror's silver plating or is reflected away from the main image. Since silver oxidizes, a silver mirror can wear out. But if we utilize TIR to reflect light, it will be everlasting.

Now that we understand the advantages of T.I.R., how is it used in throughout the world?

Total Internal Reflection is used in high quality optical devices like periscopes, or expensive binoculars and cameras.
All of the light is reflected with T.I.R. Due to this, it is a fundamental part of fiber optic transmission, one of the fastest ways of transmitting information.

See! Physics isn't useless after all! Due to Total Internal Reflection, scientists have developed fiber optic cables which are transmitting THIS VERY PAGE over the internet!

We have seen that Total Internal Reflection is one way of reflecting light. Unfortunately, it is very expensive and can only be used in the few applications that warrant the cost. Instead of TIR, mirrors are an inexpensive alternative to reflecting light.

There are three main types of mirrors:

Plane or Flat Mirrors. (Like the one in your bathroom)
Spherical Mirrors - Convex, Concave.
Parabolic Mirrors.

The function of parabolic and concave mirrors are to concentrate or focus the light.

In a parabolic mirror, all of the incoming light is focused to a point.
In a concave mirror, most of the incoming light gets focused to a point, but a few rays are not, because the curve is not in the shape of a perfect parabola.

A mirror can be broken down into the following components seen in the diagram.

It should be noted that the distance between the vertex and the focus is sometimes called the focal length. An easy way to tell a convave mirror from a parabolic mirror is the focal length. In a concave mirror, the focal length will always be equal to the radius divided by two.

f = R/2

If this formula is NOT true, then it is not a concave mirror, but a true parabolic mirror.

When dealing with mirrors, two types of images can be formed.

Real: whose reflected rays actually recombine to form the image and can be formed on a screen.
Virtual: An image whose rays appear to originate on the other side of the mirror and cannot be formed on a screen.

So if the reflected image seems to be on the same side of the mirror as the original image- you have a real image. If it seems to be on the other side of the mirror, it is virtual. Plain or Flat mirrors always produce virtual images. When you go into the washroom to brush your teeth, the image in the mirror is a virtual one. (Your counterpart seems to be on the other side of the mirror. Don't be confused by this- the person in the mirror is NOT real. )

Convex mirrors are really just concave mirrors working in reverse. Instead of the light striking the "inside" of the lens, it strikes the outside. Concave mirrors always produce virtual images.

It is important to understand the difference between concave and convex mirrors as they vary in a few key factors.

Concave: 1. Form Real AND Virtual Images 2. Images can be upright or upside down. 3. Can enlarge or reduce.	Convex: 1. Form Virtual Images ONLY 2. Images can only be upright. 3. Can reduce only.
Both Convex and Concave mirrors employ the Curved Mirror Equation which will be looked at the end of this lesson.

Magnification can be defined as the enlarging or reducing of an object. It is represented by an "M" and can be found using the following equations.

M = h1/h0

M = - d1/d0

'h1' is the height of the image reflected by the mirror.
'h0'is the height of the object.
'd1' is the distance of the image from the vertex of the mirror and is multiplied by -1.
'd0' is the distance of the object from the vertex of the mirror.
Note: A negative magnification means that the object is inverted.

Example Problem
If the height of the object is 2 m and the image is 4 m, what is the magnification?

Given:

hi = 2 m

ho = 4 m
Formula:

M = hi/ho
Process:

M = 4 m / 2 m

= 2x or 200 %
Answer:

The magnification of the object is 2x or 200 %.

When the magnification is known, one can determine a number of helpful things that make visualizing the image easier. For example, if the absolute value of the magnification is greater than 1, then the image is larger than the object.

| M | > 1     Image is larger than object.
0 < | M | < 1     Image is smaller than object.
0 > M      When "M" is less than zero, the image is inverted.

Wait a minute! What does it mean if d1 works out to be a negative number? No, you didn't screw it up, don't go bashing your head against a wall. It means that d1 is on the non-reflecting side of the mirror.

The Curved Mirror Equation applies to both concave and convex mirrors. It is called the curved mirror equation because it is an equation involving a curved mirror. That shouldn't be too hard to remember. It is used to determine either the distance of the object, image or focus from the vertex. Used in conjunction with the magnification equations, it can also be used to find the height of the object or image.

1/do + 1/di = 1/f

do represents the distance of the object to the vertex of the mirror (as seen before).
di represents the distance of the image to the vertex of the mirror (as seen before).
f represents the focal length.

Example Problem

A 2 cm tall statue is placed 20 cm from a converging mirror, whose radius is 30 cm. Find di and hi.

Given:

ho = 2 cm

do = 20 cm

Radius = 30 cm, therefore the focal length is R/2, f = 15 cm

Formula:

1/do + 1/d i = 1/f

M = hi/ho

Work:

a) Find di using Curved Mirror Equation

1/20 cm + 1/di = 1/15 cm

Find a common denominator and multiply through. In this case, 60 could be used.

3di + 60 = 4 di

Isolate the 'di'

60 cm = di

b) Now that "di" has been found, the magnification formula can be used. This will allow us to then use the height of the object coupled with the magnification to find the height of the image.

M = -di/do,
M = -60cm/20cm,
M = -3x
Now use -3x and ho to find hi
M = hi/ho,
-3x = hi / 2cm,
-6cm = hi

Answer:

The image is located 60 cm from the vertex and is -6 cm tall. This means that the object is a real and inverted image.