Refraction and lenses

Why is it that when you dip a pencil in a jar of water, the pencil appears to bend?

Refraction

A change in direction of waves crossing a boundary between two different media. It is caused by the change in speed experienced by a wave when it changes medium.

In which direction is the light ray bent?• Light Traveling from a Slow to a Fast MediumIf a ray of light passes across the boundary from a material in which it travels slowly into a material in which travels faster, then the light ray will bend away from the normal line.

• Light Traveling from a Fast to a Slow MediumIf a ray of light passes across the boundary from a material in which it travels fast into a material in which travels slower, then the light ray will bend towards the normal line.

Optical Density• The speed of the wave depends upon the optical density of

the material through which light travels.• The optical density of a material relates to the sluggish

tendency of the atoms of a material to maintain the absorbed energy of an electromagnetic wave in the form of vibrating electrons before reemitting it as a new electromagnetic disturbance.

• The more optically dense that a material is, the slower that a wave will move through the material.

Index of refraction• One indicator of the optical density of a material is the index

of refraction value of the material. • Index of refraction values (represented by the symbol n) are

numerical index values that are expressed relative to the speed of light in a vacuum.

where:n = index of refractionc = speed of light in a vacuum (3.0 x 108 m/s)v = speed of light in a medium

Index of refraction of different materials

Snell’s lawA formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different media, such as water, glass and air.

n1 – index of refraction of the first medium

1 – angle of incidence

n2 – index of refraction of the second medium

2 – angle of refraction

Note: Your calculator MUST be in the degree mode!

Critical angle, c

The angle of incidence that provides an angle of refraction of 90 degrees.Recall: .Replace 1 with c and let 2 = 90.

Since sin 90 = 1Then,

Therefore,

Lenses• A converging (convex) lens is a lens that converges rays of light

that are traveling parallel to its principal axis. They are relatively thick across their middle and thin at their upper and lower edges.

• A diverging (concave) lens is a lens that diverges rays of light that are traveling parallel to its principal axis. They are relatively thin across their middle and thick at their upper and lower edges.

Anatomy of a lens

Refraction Rules for a Converging Lens• 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.

Refraction Rule for a Diverging Lens• 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.

Lens/mirror equation

f is positive for convex lensesf is negative for concave lensesdo is positive on the object side of the lens

di is positive on the other side (image side) of the lens, where

images are real.di is negative on the object side of the lens where images are

virtual

Magnification

Magnification