Thin lens formula The thin lens formula relates the focal length of a lens to the object and image distances. If two of these properties are known, the third can be calculated using this formula.

Sample problem An object is placed 0.30 m from a lens with a focal length of 0.50 m. Where is the image located?

Sample problem An object is placed 0.30 m from a lens with a focal length of 0.50 m. Where is the image located?

Speed of light c = speed of light = 3.0 × 108 m/s in a vacuum The speed of light is a constant, and equals the product of its frequency and wavelength: c = speed of light = 3.0 × 108 m/s in a vacuum f = frequency (Hz) λ = wavelength (m)

Frequency and color The frequency of light determines its color.

Frequency and color Frequency Redder light has lower frequency and longer wavelengths. Bluer light has higher frequency and shorter wavelengths.

What is dispersion? White light is a mixture of all the colors of the rainbow. Dispersion is the process of separating these colors so that they become visible. One way to accomplish this is to use a prism to refract the light.

Speed depends on the medium Light also “bends” as it enters a new media and changes speed.

What changes as light refracts? Light waves change speed as they pass from one medium to another. If speed changes, then frequency or wavelength must also change. Frequency can’t change. Wavelength does change as light enters a new medium! Point out that the shorter wavelength is visible in the figure.

Polarization Try oscillating a string through a slit cut in a piece of cardboard. If the oscillations are in the direction of the slit, they pass through.

Polarization Try oscillating a string through a slit cut in a piece of cardboard. If the oscillations are in the direction of the slit, they pass through. If the slit is perpendicular to the direction of oscillations, they are stopped altogether. This is analogous to polarization.

Polarization of light Imagine light as a wave that is oscillating vertically—up and down. If the light waves encounter a vertical narrow slit, then they can pass through. If the waves encounter a horizontal slit, then they will be blocked.

Polarizing filters If you look at this polarized light through vertically polarizing filters, glare from light reflected off the surface is blocked, and you can see into the water. Polarizing filters are used in sunglasses, cameras, and film to reduce glare. Reflected light is filtered out by the polarizing film on the upper left side of the container.