Optical Density - a property of a transparent medium that is an inverse measure of the speed of light through the medium.(how much a medium slows the speed of light)

Optical refraction - bending of light rays as they pass obliquely from one medium to another of different optical density.

The angle between the incident ray and the normal is the angle of incidence, i. The angle between the refracted ray and the normal is the angle of refraction, r.

The ratio of the speed of light in a vacuum to its speed in a substance is the index of refraction for that substance.

Index of refraction =“c” in vacuum / “c” in substance

Snell’s Lawn = sin i / sin r

n1 sin1 = n2sin2

A ray of light passes from air into water, striking at an angle of 25.0° to the normal. The index of refraction of water is 1.33. Calculate the angle of refraction of the ray of light.

The index of refraction is a constant physical property of a substance. It can be measured using a refractometer.

Three Laws of Refraction:1. The incident ray, the refracted ray, and the normal at the point of incidence are all in the same plane.

2. The index of refraction for any homogeneous medium is a constant that is independent of the angle of incidence.

3. When a ray of light passes obliquely from a medium of lower optical density to one of higher optical density, it is bent toward the normal to the surface. A ray of light passing from a medium of higher optical density to one of lower optical density is bent away from the normal to the surface.

Wavelength effects the refraction of light. Violet light is bent more than red light and the other colors fall in between. This is why a prism splits light into its component colors.

Converging lens - convex lens, thicker in the middle than at the edges.

Diverging lens - concave lens, thicker at the edges than in the middle.

The principal axis passes through the two centers of curvature of the two surfaces of the lens.

Rays that are parallel to the PA converge at the principal focus of the lens. If they actually pass through this point it is a real focus.

If rays do not pass through a principal focus, it is a virtual focus.

The positions of the foci on the principal axis depend on the index of refraction of the lens.The focal length of a lens is the distance between the optical center of the lens and the principal focus.

Parallel rays that are not parallel to the PA are focused on the focal plane.

Lenses vs. mirrors:1. Secondary axes pass through the optical center of a lens and not through either of its centers of curvature.

2. The principal focus is usually near the center of curvature.

3. A real image is formed on the side of the lens opposite the object. Virtual images are formed on the same side as the object.

4. Convex lenses form images like concave mirrors, concave lenses form images like convex mirrors.

Images formed by rays passing through the edges of lenses are not focused at the principal focus.

This blurring of the image is called spherical aberration.

The f-number is the light gathering power of a lens.If the speed of the lens is f/4, the focal length is 4 times its effective diameter. An f/4 is four times as fast as an f/8, and 16 times as fast as an f/16.

Images formed by converging lenses:

Case #2 Object at a finite distance beyond the twice the focal length

Case #3 Object at a distance equal to twice the focal length

Case #4 Object between one and two focal lengths

Case #5 Object at principle focus

Case #6 Object at a distance less than one focal length away

Diverging lenses

Lens equations:

1/f = 1/do + 1/di

hi / ho = di / do

do and di are positive for real objects and real images

do and di are negative for virtual objects and virtual images

f is positive for converging lenses

f is negative for diverging lenses

Ex. 8 - A 1.70-m tall person is standing 2.50 m in front of a 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 height of the image on the film.

Ex. 9 - An object is placed 7.10 cm to the left of a diverging lens whose focal length is f = -5.08 cm. (a) Find the image distance and determine whether the image is real or virtual. (b) Obtain the magnification.