Snell’s Law, the Lens and Mirror Law

and Ray Diagrams

Angle of Refraction• Figuring out the angle of refraction is not as easy as figuring out

the angle of reflection.

• This is because the angle of refraction depends not only on the angle of incidence, but also on the indices of refraction of the media on either side of the boundary.

Snell’s Law

• There is a formula that governs the refraction of light as it passes from one medium to another.

• This formula is called Snell’s Law:

Recall the lab we did:• In the lab, we found the index of refraction of a liquid (water or oil)

using Snell’s Law.

• n1=1.00 (air)

• n2=?

• 1.00*sinѲi=n2*sin Ѳr• y=ax -The slope of the line we found is

equal to n2.

i

r

path of light

refractive medium

normal

Solving Snell’s Law Problems• Before we solve any problems, let’s recall what we know about

the operation SINE.

• Sin is an operation that turns an angle into a ratio between two sides in a right triangle.

• Sin-1 turns that ratio back into the angle that corresponds with it. This is the opposite operation for sine.

Solving Snell’s Law Problems

• Let’s try this problem on the board together:– A laser passing through air, which has an index of

refraction of 1.00, encounters the surface of a piece of glass with an index of refraction of 1.6 at a 30 degree angle. What angle will the laser light pass through the glass at?

Critical Angle

• Try to solve Snell’s Law for Ѳ2 using these numbers:

• n1=1.98

• Ѳ1=85O

• n2=1.00• What happened? Why?

• Ѳ1 is bigger than the critical angle for medium 1. When this happens, refraction doesn’t happen, instead we get TOTAL INTERNAL REFLECTION.

Finding the Critical Angle• The formula for critical angle is derived from

Snell’s Law. Basically, it’s the point at which Snell’s Law mathematically breaks down.

c sin 1 n2n1

Types of Lenses

• Concave Lens-Is wider at the edges than in the middle.

• Concave lenses bend parallel rays of light outward, away from the focal point. We call this DIVERGENT.

Types of Lenses

• Convex lens-Fatter in the middle than at the edges.

• Convex lenses bend parallel rays of light inward, toward the focal point. We call this CONVERGENT.

Lenses and Refraction

• Lenses work because light refracts at different angles as it hits the surface of the lens:

• We could use Snell’s Law to figure out what direction a lens will bend light and to figure out where an image will occur, but that would be a pain in the butt. Yuck!

• Luckily we have a nice shortcut using Ray Diagrams.

Ray Diagrams and Lenses

• For thin lenses, we can use ray diagrams to determine where an image will appear in a lens. For example:

Rules for Convergent Lenses

• Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens.

• Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.

• An incident ray that passes through the center of the lens will in affect continue in the same direction that it had when it entered the lens.

More on Convergent Lenses

• We simply need to pick any two of those special rays to find where the image will form.

• It will form where the rays intersect.

Rules for Divergent Lenses

• Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its extension will pass through the focal point).

• Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.

• An incident ray that passes through the center of the lens will in affect continue in the same direction that it had when it entered the lens.

More on Divergent Lenses

• Like with convergent lenses, we simply need to draw any two of the special rays and find where they intersect to find where the image will appear.

Real and Virtual Images

• Real Images:– Formed at a location that light actually reaches.– Are always upside down– Can be projected on a screen– Are only produced by converging lenses and mirrors.

• Virtual Images:– Formed at a location where the light appears to come from,

the light isn’t actually traveling to that point.– Are always right-side up.– Cannot be projected on a screen. – Can be formed by either converging or diverging mirrors

and lenses.

Converging Lenses Revisited

• Real Images form in converging lenses when the object is farther from the lens than the focal point.

Converging Lenses Revisited (cont)

• Virtual Images form in converging lenses when the object is closer to the lens than the focal point.

Converging and Diverging Mirrors

• Concave Mirrors are CONVERGING, and act like Convex Lenses

• Convex Mirrors are DIVERGING and act like Concave Lenses

Lens and Mirror Diagram

• Both Lens and Mirror problems can be solved using the same formula:

• f=focal length• do=distance between object and lens or mirror

• di=distance between image and lens or mirror

Rules for the Lens and Mirror Formula• These are on your formula sheet, so you don’t need to copy them.

• Do you notice any patterns that can help determine if an image will be virtual or real?

• Why do you think the focal length of a diverging lens or mirror is always negative?

• What happens when f=do to make it so no image forms?