Light

Light is a form of electromagnetic radiation. Light waves travel in a straight line. A changing electric field produces a changing magnetic field and, a changing magnetic field produces a changing electric field. An electromagnetic wave is one in which a varying electric field is accompanied at right angles by a varying magnetic field.

Light waves have wavelengths from about 400 nm (4.00 x 10-7 m) to about 700 nm ( 7.00 x 10-7 m).

The approximate speed of light in a vacuum is found to be 3.00 x 108 m/s. The speed of light is designated as c rather than v and is related to wavelength and frequency by the following equation,

c = f8

A light source, or body that emits light, is termed luminous. A body that reflects light is illuminated. The rate at which a body emits light depends on the rate at which it puts energy into it. This rate is called luminous flux (P) and the unit of luminous flux is the lumen (lm). The rate of light that falls on a unit surface area is called illuminance (E). The relationship between the flux and the illuminance is

E = P/4Bd²

where E is the illuminance, P represents the luminous flux, and d is the distance from the surface.

Materials that transmit light waves (allow them to pass through) are termed transparent. Materials that allow light waves through them but objects cannot be clearly seen through them are translucent. If a material absorbs or reflects all light waves are called opaque. The primary colorsof light are red, green, and blue. The correct combination of red, green, and blue will produce white light.  Mixing a pair of primary colors will produce secondary light colors as follows:

Red + Blue = Magenta

White light can also be produced by mixing one primary color with its complementary secondary color (e.g., Yellow + Blue = White). Cyan and red are complementary. Magenta and green are complementary. The color of an object depends on the wavelength of light that is reflected off an object.

Ordinary light contains electromagnetic waves vibrating in every direction perpendicular to its direction of travel. If polarizing material is placed in a beam of light, only waves that vibrate in the plane of the polarizing material can pass through. Light that is reflected by various objects and scattered by air is glare.

Light waves obey the Law of Reflection which states that the angle of reflection is equal to the angle of incidence. Thus, the angle that light bounces off something (reflection) is equal to the angle that light hits the surface of something (incidence). Refraction is the bending of light rays at the boundary between two media and occurs only when the incident ray strikes the boundary at an angle. The Index of Refraction is the ratio of c in a vacuum to c in a medium. Dispersion is the separation of light into a spectrum by refraction.

Snell's Law states that when light goes from a medium with small n (index of refraction) to one with large n, it is bent toward the normal. Light going from materials with a large n to those with a small n is bent away from the normal. Snell's Law may be written as

n = sin Øi/sin Ør

where Øi is the angle of incidence and Ør is the angle of refraction. In general, for a ray traveling from one medium into another, Snell's Law may be written as

nisinØi = nrsinØr

where ni is the index of refraction of the incident medium and nr is the angle of refraction of the second medium.

Total internal reflection occurs if light is incident on a boundary from the medium with the larger index of refraction. If the angle of incidence is greater than the critical angle, no light leaves; it is all reflected. Total internal reflection also occurs when light passes from a more to a less dense medium at an angle greater than the critical angle. Light waves of different wavelengths have slightly different refractive indices. Thus, they are refracted at different angles. Light falling on a prism is dispersed into a spectrum of colors.

Review Questions:

1. How long does it take for light to reach the earth from the moon? The moon is 3.8 x 10⁸ m away.

1.3 s

2. An alien zaps Octavio with a laser that has a wavelength of 514 nm. What is the frequency of the laser?

5.84 x 10*14 Hz

3. Hess becomes a mad scientist, creating a laser weapon that creates a pulse of light that lasts only a few femtoseconds. (a) What is the length of a pulse of violet light that lasts 6.0 fs? (b) How many wavelengths of violet light are included in such a pulse? The wavelength of violet light is 400 nm.

4. How many minutes does it take for light from the sun to reach the earth? The sun is 1.5 x 108 km away.

5.0 x 10*2 s or 8.3 minutes

5. Jeanique wants to know how much luminous flux is needed to illuminate her desk at home to 160 lux to keep her from getting eye strain. Her lights are 2.0 m above her desk. What is the minimum luminous flux her lights must deliver to meet her needs?

8.0 x 10*3 lm

6. Abby has a three-way bulb by her desk at home that uses 50, 100, and 150 W of electrical power to deliver 665, 1620, and 2285 lm in its three settings respectively. If the bulb is 80 cm above her paper and she needs at least 175 lux to see properly, what is the minimum setting that should be used on the bulb?

P = 1.4 x 10*3 lm so must use 100W setting.

7. Tomeko gets a ring from her boyfriend that tells her it is a diamond ring. She knows that a diamond has an index of refraction of about 17° when light is shined on it at 45°. The angle of incidence in air is 1.00. Is her ring a real diamond?

Angle of refraction is 17 degrees so diamond is real.

8. Roberto creates a completely transparent material that will slow down the speed of light to 2.0 x 108 m/s. What is its index of refraction?

9. Josh accidentally fires his laser at home that bounces of a mirror and strikes his aquarium which contains a rare, exotic fish valued at \$10,000. The fish is floating 32° to the normal. Will his fish be fried by his laser or live?

Angle of refraction for glass is 25 degrees; angle of refraction for water is 29 degrees. The fish lives!

10. Galdis has a swim party at her house. The pool light is 1.5 m away from the edge of the pool and 2.0 below the surface of the pool. The pool is filled to the top with water. (a) At what angle does the light reaching the edge of the pool leave the water? (b) Does the pool light appear deeper or shallower than it really is?

angle of incidence is 37 degrees; angle in air is 53 degrees; light appears to be 1.1 m so appears more shallow.

Honors:

11. Suppose Maxwell and David bet each other that their lasers are the fastest. David says he can fire a pulse in air and still beat Maxwell who fires his in a vacuum. Taryl says her detectors require a time difference of 10 ns. How long would the race have to be to determine a winner?

10*4 m or 10 km

12. Amanda wants to compare the luminous flux from a bulb with that of a 1750 lm lamp. The two bulbs illuminate a sheet of paper equally. The 1750 lm lamp is 1.25 m away and the unknown bulb is 1.08 m away. What is its luminous flux?

1.31 x 10*3 lm

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