Bendy, Bouncy, Beautiful! The Path Light Travels Bendy, Bouncy, Beautiful!

When light bends instead of bounces Refraction When light bends instead of bounces

Refraction Often, light will not travel in a straight line when it crosses from one transparent medium into another This is due to the fact that light changes speed when it enters a new medium. The degree to which it bends is called the angle of refraction; it is measured between the light ray and the normal.

Why does light refract? Well, I don’t know why a change in speed would cause a light beam to swerve from its path But I do know a good metaphor for it, a metaphor I call the Four Wheel Drive Photon Metaphor

Rules of Thumb Light bends toward the normal when it slows down and away from the normal when it speeds up The greater the change in speed, the greater the refraction

The Refraction Equations The angle of refraction can be found using this equation: Sin 2 / sin  1 = 2 /  1 Where 1 and 2 are the two media and  is the speed of light in the respective media The angles can be incidence and refraction, or 2 refraction angles (to compare two media)

Try this problem: Through which medium does light travel fastest?

Answer: Sin glass / sin water = vglass /vwater Sin 34.5 / sin 40.6 = v2/v1 0.57/ 0.65 = v2/v1 Therefore, vgalss < vwater Also, you can see that it bends more in glass, so it must be slowing down more in glass

Now, try this: How many times faster does light travel through water than it does through glass?

Answer: Since we want to find out how much faster the speed is in water, vwater /vglass = sinwater /singlass 0.65/0.57 = 1.15, so, it travels 0.15 times faster, or 15% faster

Important item: wavelength, frequency, and refraction As the light changes speed, what happens to the frequency of the light? Think: if the light changed frequency, how would you know? It would change color. So, does the frequency change? Nope!

Important item: wavelength, frequency, and refraction The light wave changes speed but doesn’t change frequency. Therefore, what must happen to the wavelength of the light as it goes from space through any other medium? It must get shorter Think about what happens to the distance between cars on a freeway when the speed of traffic slows down

Index of refraction, n n = c/  The index of refraction, n, is the ratio of the speed of light in a vacuum to the speed of light in a transparent medium: n = c/ 

What is the index of refraction in air? Well, light slows down an itty, bitty, teeny, weeny little bit in air. Basically, the speed in air = the speed in a vacuum nair = c/v nair = 3.00 x 108 ms-1/ 3.00 x 108 ms-1 nair = 1.00 Question: what are the units to use?

Snell’s Law - a combination of the preceding equations Indices of refraction for materials are found in published tables. You can use them to find the path of light through various media using this equation: n1 sin1 = n2 sin  2 The angles are those of incidence and refraction, respectively

n1 sin  1 = n2 sin  2 2 n2 n1 1

Practice Problem If nair is 1.00 and nwater is 1.33, then light entering a pond at an angle of 60° to the normal would travel at what angle to the normal through the water?

Answer: n1 sin  1 = n2 sin  2 (1.00) sin 60 = 1.33 (sin x)

Let’s check:

Puzzler You see a fat, juicy fish in a pond. You are hungry. You throw a rock right at that fish. If your aim is true, do you hit the fish?

Fish Puzzler #1

Draw the light ray from fish to eye

Draw the light ray from fish to eye

Trace the thought line backwards

The stone misses the fish

Puzzler: Where to spear the fish? We already know that if you throw a spear directly at a fish you see under water, the spear will go over its head And, the deeper the fish, the greater safety zone it has if you throw straight at the image So, how do you get that fish?

The thought rays meet at  1 refraction  2 incidence

Equivalent angles  1 refraction  2 incidence

Quick n dirty:  1 refraction  2 incidence Apparent depth = real depth / n (water)  1 refraction  2 incidence

Dispersion - a result of refraction We already know that the amount that light refracts in a medium depends on its speed And, we know frequency doesn’t change and wavelength does So, the amount of refraction can also be considered to be dependent on the wavelength of the light

Wavelength in different media The ratio of wavelengths of light is inversely proportional to the ratio of indices of refraction. This means that, in a material with a larger index, the wavelength of light will be less. 1/ 2 = n2 / n1 This pertains to a beam of light traveling through two different media

Puzzler: Which will refract more, red light or blue light? Which color travels faster in space, red or blue? Neither! They go the same speed! Which has a higher frequency, red or blue? Blue! So, which has a shorter wavelength?

Puzzler: Which will refract more, red light or blue light? Now, the last equation had to do with one beam of light in two media. But we can also use it to compare two lights in one medium: red/ blue = nblue / nred Can you see that blue light has the larger index of refraction?

Puzzler: Which will refract more, red light or blue light? So, nblue > nred Which has a bigger refraction? Remember: n1 sin1 = n2 sin2 Rearrange: n1/ n2 = sin 2 / sin 1 Or, nblue/ nred = sin red / sin blue , so sin red > sin blue Can you see that red light bends less??

Note: light bends toward the normal when it slows down Red bends away from the straight-line path less than blue light because it has a smaller index of refraction and thus a bigger angle of refraction

Dispersion Dispersion is when refraction causes light to separate into its various wavelengths. This is commonly called the “prismatic effect” Rainbows are a product of dispersion

Critical Angle and Total Internal Reflection Total internal reflection: Light reflects completely at an interface, back into the medium with the higher refractive index. Critical angle: The minimum angle of incidence at which total internal reflection occurs.

Why does this happen? As the angle of incidence increases, the angle of refraction will also increase n1 sin1 = n2 sin  2 the indices of refraction stay the same At some point, the index of refraction will equal 90°

Critical angle: from water to air Note: light bends away from the normal when it speeds up

air water

air water  refracted The angle of reflection  refracted is 90° to the normal, parallel with the surface of the water. No light escapes. This is the critical angle,  c

When i > c, light does not escape the medium air Total internal reflection water

Solving problems with  c To find the critical angle, use Snell’s law and substitute 90° in for  refracted n1 sin c = n2 sin  refracted The sine of 90° is 1, so  refracted = 1 n1 sin  c = n2 1 Or, sin  c = n2/n1