Dispersion• The spreading of light into its color

components is called dispersion.• When light enters a prism, the refracted

ray is bent towards the normal, and when it leaves the prism, it is refracted away from the normal.

Dispersion• The refractive index of glass depends on

the wavelength of light (see p. 809)• This means that different colors get

bent by different amounts and depart a prism traveling in different directions… resulting in a rainbow

The physics of rainbows• Rainbows occur because light is

refracted as it enters and leaves a water droplet.• the index of refraction depends on the

color (wavelength), so each color is bent a different amount.

The physics of rainbows• From each droplet we see only one color, since it

is the only ray traveling in the direction to our eye.• But every droplet reflects at the same angle for a

given color (wavelength)• The position of the droplet, relative to our eye,

determines which color we see.

Thin Lenses• Lenses are made of transparent materials that

refract light in such a way that an image of the source of the light is formed.

• We assume that the lens is so thin compared to the focal length (f) that it makes no difference whether f is measured between the focal point and either surface of the lens, or the center of the lens.

Converging Lens• Converging lens: paraxial rays (rays near the

principle axis) that are parallel to the principal axis converge to the focal point F after passing through the lens.

• For an object that is infinitely far away, the image is formed at the focal point (F)

Diverging Lens• Diverging lens: causes infinite parallel rays to

diverge after exiting the lens.• Paraxial rays that are parallel to the principal axis

appear to originate from a single point on the axis after passing through the lens.

• This point is the focal point (F) and its distance from the lens is the focal length (f)

Diverging Lens• Diverging lens: causes infinite parallel rays to

diverge after exiting the lens.• Paraxial rays that are parallel to the principal axis

appear to originate from a single point on the axis after passing through the lens.

• This point is the focal point (F) and its distance from the lens is the focal length (f)

Ray Tracing to find images• Just like with curved mirrors, we can use ray

tracing to locate the image formed by thin lenses.

Ray Tracing to find images• Just like with curved mirrors, we can use ray

tracing to locate the image formed by thin lenses.

The thin lens equation•

Sign Conventions for lenses• f is + for converging lens• f is – for diverging lens• di is + for a real image formed to the

right of the lens• di is – for a virtual image formed to the

left of the lens• m is + if image is upright• m is – if image is inverted

Example 1 Converging LensA person 1.70 m tall is standing 2.50m in front of a digital camera. The camera uses a converging lens whose focal length is 0.0500 m.a) Find the image distance and

determine whether the image is real or virtual.

b) Find the magnification and the height of the image.

Example 1 Converging LensA person 1.70 m tall is standing 2.50m in front of a digital camera. The camera uses a converging lens whose focal length is 0.0500 m.a) Find the image distance and

determine whether the image is real or virtual.

b) Find the magnification and the height of the image.

Example 2 Diverging LensAn object is placed 7.10cm to the left of a diverging lens whose focal length is f=-5.08cma) Find the image distance and

determine whether the image is real or virtual

b) Obtain the magnification

Assignment

Problems p. 837 #44, 46, 50, 51, 55