Chapter 16 Light Waves and Color

Properties of Light Waves (and all other waves) Polarization Reflection Refraction Interference Diffraction

Polarized Light How do polarizing sunglasses and camera filters work? What is polarized light? Recall that light is an electromagnetic wave consisting of oscillating electric and magnetic fields:

The oscillating electric field vector shown is in the vertical plane, and the magnetic field is horizontal. Actually, the electric field could oscillate in the horizontal with the magnetic field in the vertical plane, or the electric field could oscillate at some angle to the horizontal. As long as the electric field is always pointing in the same direction for all the waves, the light is polarized.

Unpolarized light has random directions of orientation. The electric field vector oscillates in a single direction for polarized light. Unpolarized light has random directions of orientation. Light is usually produced unpolarized. To make light polarized, something must occur to select just one direction of field oscillation.

Polarizing filters allows only that component of each electric field vector that is aligned with the filter’s axis of transmission to pass through. The component perpendicular to this axis is absorbed.

Reflection from a smooth surface of a transparent material such as glass or water can also polarize light. Incoming sunlight is unpolarized. When the angle between the reflected wave and the transmitted wave is a right angle, the reflected wave is polarized. Polarizing sunglasses can help reduce glare from reflected sunlight.

Many interesting and colorful effects are related to the phenomenon of birefringence. Birefringence is also called double refraction. Light with different polarizations travels with different velocities when passing through a birefringent material. This causes colorful displays when the birefringent material is viewed through crossed polarizers. Calcite crystals are a good example of birefringent material. Lines are doubled when viewed through a calcite crystal.

Many interesting and colorful effects are related to the phenomenon of birefringence. Birefringence is also called double refraction. Light with different polarizations travels with different velocities when passing through a birefringent material. This causes colorful displays when the birefringent material is viewed through crossed polarizers. A plastic lens under compression shows stress birefringence when viewed between crossed polarizers.

Reflection of light by a flat mirror Consider plane wavefronts (no curvature) approaching a flat mirror at an angle: After reflection they travel away from the mirror with the same speed as before reflection. Some parts of the wavefront are reflected sooner than others. The reflected wavefronts have the same speed and spacing but a new direction. The angle between the wavefronts and the mirror is the same for the emerging wave.

Law of Reflection We usually measure the angles with respect to the surface normal, a line drawn perpendicular to the surface of the mirror. The angle of incidence is equal to the angle of reflection.

Refraction of Light What happens to light rays when they encounter a transparent object such as glass or water? The speed of light in glass or water is less than in air or vacuum. Thus, the distance between wavefronts (the wavelength) will be shorter. The index of refraction is the ratio of the speed of light c in a vacuum to the speed of light v in some substance.

Since the wavefronts do not travel as far in one cycle, the rays bend (much like rows in a marching band bend when one side slows down by taking smaller steps). The amount of bending depends on the angle of incidence. It also depends on the indices of refraction of the materials involved. A larger difference in speed will produce a larger difference in indices of refraction and a larger bend in the wavefront and ray.

Law of Refraction When light passes from one transparent medium to another, the rays are bent toward the surface normal if the speed of light is smaller in the second medium, and away from the surface normal if the speed of light is greater. For small angles:

Interference of Light Waves Is light a wave or a particle? If it is a wave, it should exhibit interference effects: Recall that two waves can interfere constructively or destructively depending on their phase.

Light from a single slit is split by passing through two slits, resulting in two light waves in phase with each other. The two waves will interfere constructively or destructively, depending on a difference in the path length. If the two waves travel equal distances to the screen, they interfere constructively and a bright spot or line is seen.

If the distances traveled differ by half a wavelength, the two waves interfere destructively and a dark spot or line appears on the screen. If the distances traveled differ by a full wavelength, the two waves interfere constructively again resulting in another bright spot or line. The resulting interference pattern of alternating bright and dark lines is a fringe pattern.

Red light with a wavelength of 630 nm strikes a double slit with a spacing of 0.5 mm. If the interference pattern is observed on a screen located 1 m from the double slit, how far from the center of the screen is the second bright line from the central (zenith) bright line? = 630 nm = 6.3 x 10-7 m d = 0.5 mm = 5 x 10-4 m x = 1 m

Similarly, interference can occur when light waves are reflected from the top and bottom surfaces of a soap film or oil slick. The difference in the path length of the two waves can produce an interference pattern. This is called thin-film interference.

Different wavelengths of light interfere constructively or destructively as the thickness of the film varies. This results in the many different colors seen.

The thin film may also be air between two glass plates. Each band represents a different thickness of film.

Diffraction and Gratings The bright fringes in a double-slit interference pattern are not all equally bright. They become less bright farther from the center. They seem to fade in and out. This effect, called diffraction, is due to interference of light coming from different parts of the same slit or opening.

When the path difference between light coming from the top half of the slit and that coming from the bottom half is 1/2 of a wavelength, a dark line appears on the single-slit diffraction pattern. The position of the first dark fringe is:

Light with a wavelength of 550 nm strikes a single slit that is 0 Light with a wavelength of 550 nm strikes a single slit that is 0.4 mm wide. The diffraction pattern produced is observed on a wall a distance of 3.0 m from the slit. What is the distance from the center of the pattern to the first dark fringe? = 550 nm = 5.5 x 10-7 m w = 0.4 mm = 4 x 10-4 m x = 3.0 m

How wide is the central bright fringe of this diffraction pattern? The central bright fringe extends out to the first dark fringe on either side, so its width is just twice the distance y: = 550 nm = 5.5 x 10-7 m w = 0.4 mm = 4 x 10-4 m x = 3.0 m

The diffraction pattern produced by a square opening has an array of bright spots. Looking at a star or distant street light through a window screen can produce a similar diffraction pattern.

A diffraction grating has a very large number of slits very closely spaced. Whenever the path difference is equal to an integer multiple of the light wavelength, we get a strong bright fringe for that wavelength. Different wavelengths will appear at different points on the screen, spreading the light into its spectrum. Diffraction gratings in spectrometers are used to separate and measure the wavelengths of light. Gratings also produce the effects seen in novelty glasses, reflective gift wrappings, and in the colors seen on a CD.

Wavelength and Color How do we perceive ? What causes different objects to have ? Why is the sky ? color different colors BLUE

Newton demonstrated that white light is a mixture of colors. He showed that white light from the sun, after being split into different colors by one prism, can be recombined by a second prism to form white light again.

How do our eyes distinguish color? Light is focused by the cornea and lens onto the retina. The retina is made up of light-sensitive cells called rods and cones. Three types of cones are sensitive to light in different parts of the spectrum.

S cones are most sensitive to shorter wavelengths. M cones are most sensitive to medium wavelengths. L cones are most sensitive to longer wavelengths. The sensitivity ranges overlap, so that light near the middle of the visible spectrum will stimulate all three cone types. Light of 650 nm wavelength stimulates L cones strongest and S cones weakest; the brain identifies the color red.

Color Mixing The process of mixing two different wavelengths of light, such as red and green, to produce a response interpreted as another color, such as yellow, is additive color mixing. Combining the three primary colors blue, green, and red in different amounts can produce responses in our brains corresponding to all the colors we are used to identifying. Red and green make yellow, blue and green make cyan, and blue and red make magenta. Combining all three colors produces white.

Color Mixing The pigments used in paints or dyes work by selective color mixing. They absorb some wavelengths of light more than others. When light strikes an object, some of the light undergoes specular reflection: all the light is reflected as if by a mirror.

Color Mixing The selective absorption of light is a form of subtractive color mixing. In color printing, the three primary pigments are cyan, yellow, and magenta. Cyan absorbs red but transmits and reflects blue and green. Yellow absorbs blue but transmits and reflects green and red. Magenta absorbs at intermediate wavelengths, but transmits and reflects blue and red.

Why is the sky blue?

The white light coming from the sun is actually a mixture of light of different wavelengths (colors). The longer wavelengths of blue light are scattered by gas molecules in the atmosphere more than shorter wavelengths such as red light. The blue light enters our eyes after being scattered multiple times, so appears to come from all parts of the sky.

Why is the sunset red?

The shorter wavelengths of blue light are scattered by gas molecules in the atmosphere more than longer wavelengths such as red light. When the sun is low on the horizon, the light must pass through more atmosphere than when the sun is directly above. By the time the sun’s light reaches our eyes, the shorter wavelengths such as blue and yellow have been removed by scattering, leaving only orange and red light coming straight from the sun.