1 By Mike Maloney © 2003 Mike Maloney2 Light as a Ray Light very often travels in straight lines. We represent light using rays, which are straight lines

1

By Mike Maloney

© 2003 Mike Maloney 2

Light as a Ray

Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric optics.


Light as a Ray

When the source of light is very far away (like the sun) we can assume that the rays are all coming in parallel to each other.

In other cases, they radiate out fromthe source in all direction.


Reflection

• We know that when a wave meets a boundary (change in medium), part of it gets reflected.

• The same is true for light waves … if they didn’t we wouldn’t really see anything at all.

• When a light wave meets a boundary with something that is opaque, it is reflected.


Reflection

Law of reflection: the angle of reflection (that the ray makes with the normal to a surface) equals the angle of incidence.


Reflection

• The law states that the angle that a light ray is reflected is equal to the angle it hits the surface at (aka angle of incidence.

• Or in laymen's terms, the angle the light leaves the surface at is the same as the angle that it hits the surface at.


Reflection

• If all opaque objects reflect light, how come I can’t see my image in the wall or your shirt, but I can in a mirror?

• Because all surfaces are not flat, even the ones that look like they are.

• Regular (Specular) Reflection, is the kind that you see when you look in a mirror.

• All the light rays reflect parallel to each other, so the reflected image looks the same, just flipped left to right.

• Diffuse Reflection is what happens when the surface is not flat. The reflected light rays do not end up parallel to each other.


Diffuse Reflection

When light reflects from a rough surface, the law of reflection still holds, but the angle of incidence varies. This is called diffuse reflection.


Diffuse Reflection

With diffuse reflection, your eye sees reflected light at all angles. With specular reflection (from a mirror), your eye must be in the correct position.

Diffuse Reflection Specular Reflection


Perception and Reflection

What you see when you look into a plane (flat) mirror is an image, which appears to be behind the mirror.


Refraction

• Have you ever looked at your legs in a pool …or looked at a pencil in a glass of water?

• You may notice that they seem to bend.

• This phenomenon is called REFRACTION.

• Can you guess why it might happen?HINT: remember light is a wave …


Refraction

• When light passes from one medium to another at an angle it seems to bend.

• This is due to the fact that it slows down or speeds up when it changes mediums.

• n (index of refraction) is an experimental number used to compare different materials to each other based on how much they slow down light.

• n = (speed of light in vacuum) / (speed of light in medium)

• n = c / v = o /

• n is always bigger than 1.

Why is this true?

Why is this true?


Some indices of Refraction

What happens to the wavelength of light when it enters a new medium?

BACK


Less Dense to More Dense

• When light travels from a less dense to a more dense medium and does not hit is straight on, it slows down and bends towards the center.


More Dense to Less Dense• And what do you think happens when you go from

more dense to less dense?• Right it speeds up and bends away from the

middle.


Refraction

Light changes direction when crossing a boundary from one medium to another. This is called refraction, and the angle the outgoing ray makes with the normal is called the angle of refraction.


Refraction

• Different materials bend light at different amounts

• n (index of refraction) can also be used to compare different materials to each other based on how much they bend light.


Snell’s Law

• A ray of light bends in such a way that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, and this constant is the index of refraction.

• OR,

n = Sin Θi

Sin Θrn = index of refractionΘi = angle of incidence (incoming angle)Θr = angle of refraction (outgoing/bent angle)** NOTE this equation is only good when the light is incident in air or a vacuum.


Snell’s Law

• nr / ni = sin Θi / sin Θr

Or by playing with the math

• n1 sinΘ1 = n2 sinΘ2

• In this equation n1 and n2 are the index of refractions of each material, and Θ1 and Θ2 are the corresponding angles.

• Θ is always measured from the normal line.

• Let’s try an example.


Why are you short in water?

Refraction is what makes objects half-submerged in water look odd.


Total Internal Reflection

• What would happen if when light went from a more dense medium to a less dense medium and the angle of refraction was greater than 90°?

n = 1.33

n = 1.0



• What would happen if when light went from a more dense medium to a less dense medium and the angle of refraction was greater than 90°?

• You would get something called total internal reflection. The light would be refracted so much that the ray never makes it outside of the medium, and no transmission would occur.

• The light would all reflect at the same incident angle.



• As the incident angle increases, the refracted angle gets closer to 90°. The minimum angle that causes total internal reflection (Θr = 90°) between two materials

is known as the critical angle (θc).


Critical Angle ΘC

• It is found using Snell’s law and setting the angle of refraction to 90° and solving for the angle of incidence.

• n1 sinΘc = n2 sin(90°)

• If ΘC is bigger than 90°, no transmission occurs, only reflection.


Finding the Critical Angle ΘC

• Lets find the critical angle for light moving from water to air.

• nwater = 1.33, nair = 1.00

• n1sinΘ1 = n2 sin(90°)

• 1.33*sinΘ1 = 1*sin(90)

• sinΘ1 = 1/1.33 = .75

• Θ1 = sin-1(0.75)

• Θ1 = 48.6 deg


Summary of Equations

• Reflection

• Refraction

ri

r

i

v

cn

sin

sin0

2211 sinsin nn

1

2sinn

nc


Some Effects Of Refraction

• Mirages

• Prisms

• Rainbows

• Lenses

• Fiber-optics


Mirages

• The high temperature near the ground changes the index of refraction of the air near the ground.

• This makes the light curve or refract.

• If it is hot enough, the light coming down can curve back up into your eyes and you see a “fake” reflection.


Prisms

• Different wavelengths of light have slightly different indices of refraction.

• When white light moves through a prism all the colors get refracted twice, each by a slightly different amount.

• When they emerge they are no longer on top of each other, but are now separated (dispersed).


Rainbows


Rainbows Explained

• Different colors of light get diffracted different amounts when they travel through water.

• This causes a spectrum of light to appear in the sky when the Sun shines onto droplets of moisture in the Earth's atmosphere.

• White light enters and refracts, reflects off the back and refracts again as it comes out. The various colors have been refracted different amounts and are no longer on top of each other.

• What you see is a pattern of different refracted colors from different drops (red from one drop, green from another, blue from another) in the shape of a bow that reach your eyes.

• Everyone sees a different rainbow.

http://en.wikipedia.org/wiki/File:Rainbowrays.png


Lenses

• A lens can be used to focus light.

• Depending on where on the lens the light hits, it has different incoming angle, and therefore leaves at a different refracted angle.

• If the lens is shaped right, all the waves focus on a point called the focal point.

• What is the purpose of your eyeglasses?


Fiber Optics/TV Rock

Light will be transmitted along the fiber even if it is not straight. An image can be formed using multiple small fibers.

Documents

1 By Mike Maloney © 2003 Mike Maloney2 Light as a Ray Light very often travels in straight lines. We represent light using rays, which are straight lines