Text book Physics; John D. Cutnell and Kenneth W. Johnson; 7 th edition; Wiley; 2007.

Electromagnetic Waves Each of the beautiful colors in this dancer’s carnival outfit corresponds to a different wavelength in the visible region of the spectrum of electromagnetic waves. (Sylvain Grandadam/Getty Images, Inc.)

 An electromagnetic wave is a transverse wave because the electric and magnetic fields are both perpendicular to the direction in which the wave travels.  An electromagnetic wave, does not require a medium in which to propagate. Electromagnetic waves can travel through a vacuum or a material substance, since electric and magnetic fields can exist in either one.  Electromagnetic waves can be produced in situations that do not involve a wire antenna. In general, any electric charge that is accelerating emits an electromagnetic wave, whether the charge is inside a wire or not.  All electromagnetic waves move through a vacuum at the same speed ‘c’. This speed is called the speed of light in a vacuum is equal to 3.00 x 10 8 m/s. In air, electromagnetic waves travel at nearly the same speed as they do in a vacuum, but, in general, they move through a substance such as glass at a speed that is substantially less than c.

Cochlear implants : Cochlear implants use the broadcasting and receiving of radio waves to provide assistance to hearing-impaired people who have auditory nerves that are at least partially intact.

Wireless capsule endoscopy : The broadcasting and receiving of radio waves is also now being used in the practice of endoscopy. In this medical diagnostic technique a device called an endoscope is used to peer inside the body. For example, to examine the interior of the colon for signs of cancer, a conventional endoscope (known as a colonoscope) is inserted through the rectum. As the capsule moves through the intestine, the transmitter broadcasts the images to an array of small receiving antennas attached to the patient’s body. These receiving antennas also are used to determine the position of the capsule within the body.

An electromagnetic wave, like any periodic wave, has a frequency f and a wavelength that are related to the speed v of the wave by v = f λ. For electromagnetic waves traveling through a vacuum or, to a good approximation, through air, the speed is v=c, so. c = f λ

An ear thermometer, like the pyroelectric thermometer shown in the figure, determines the body’s temperature by measuring the amount of infrared radiation that emanates from the eardrum and surrounding tissue.

Find the range in wavelengths (in vacuum) for visible light in the frequency range between 4.0 x Hz (red light) and 7.9 x Hz (violet light). Express the answers in nanometers. Solution: Since 1 nm = m

1.28 s, 1.9 x 10 2 s 1/2746) (a) Neil A. Armstrong was the first person to walk on the moon. The distance between the earth and the moon is 3.85 x 10 8 m. Find the time it took for his voice to reach earth via radio waves. (b) Someday a person will walk on Mars, which is 5.6 x m from earth at the point of closest approach. Determine the minimum time that will be required for that person’s voice to reach earth. (1.28 s, 1.9 x 10 2 s) 8.3 min. 2/2746) During a flare-up from a sunspot, X-rays (electromagnetic waves) are emitted. If the distance between the sun and the earth is 1.50 x m, how long (in minutes) does it take for the X-rays to reach the earth? (8.3 min.) 4.1 x m 3/2746) In astronomy, distances are often expressed in light-years. One light-year is the distance traveled by light in one year. The distance to Alpha Centauri, the closest star other than our own sun that can be seen by the naked eye, is 4.3 light-years. Express this distance in meters. (4.1 x m)

m 7/2747) A truck driver is broadcasting at a frequency of MHz with a CB (citizen’s band) radio. Determine the wavelength of the electromagnetic wave being used. ( m) 10/2747) Magnetic resonance imaging, or MRI, and positron emission tomography, or PET scanning, are two medical diagnostic techniques. Both employ electromagnetic waves. For these waves, find the ratio of the MRI wavelength (frequency = 6.38 x 10 7 Hz) to the PET scanning wavelength (frequency = 1.23 x Hz) PET = 5.18 x MRI ( λ PET = 5.18 x λ MRI ) 11/2747) The human eye is most sensitive to light having a frequency of about 5.5 x Hz, which is in the yellow-green region of the electromagnetic spectrum. How many wavelengths of this light can fit across the width of your thumb, a distance of about 2.0 cm? ( )

The Reflection of Light: Mirrors The reflection of light from the plane surface of the water acts to double the presence of this white ibis. This chapter discusses the images formed by the reflection of light from plane and spherical mirrors. (Darrell Gulin/The Image Bank/Getty Images)

(a) Portions of two spherical wave fronts are shown. The rays are perpendicular to the wave fronts and diverge. (b) For a plane wave, the wave fronts are flat surfaces, and the rays are parallel to each other.

Law of Reflection The incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of reflection θ r equals the angle of incidence θ i : θ r = θ i

(a) The drawing shows specular reflection from a polished plane surface, such as a mirror. The reflected rays are parallel to each other. (b) A rough surface reflects the light rays in all directions; this type of reflection is known as diffuse reflection.

The properties of the images formed by plane mirrors: 1. The image is upright. 2. The image is virtual. 3. The image is the same size as you are. 4. The image is located as far behind the mirror as you are in front of it. 5. The image of yourself in the mirror is also reversed right to left and left to right.

 4/2820) The drawing shows a laser beam shining on a plane mirror that is perpendicular to the floor. The beam’s angle of incidence is 33.0°. The beam emerges from the laser at a point that is 1.10 m from the mirror and 1.80 m above the floor. After reflection, how far from the base of the mirror does the beam strike the floor?

(a) When a ray of light is directed from air into water, part of the light is reflected at the interface and the remainder is refracted into the water. The refracted ray is bent toward the normal (θ 2 < θ 1 ). (b) When a ray of light is directed from water into air, the refracted ray in air is bent away from the normal (θ 2 > θ 1 ).

Snell’s Law of Refraction θ 2 θ 1 When light travels from a material with refractive index n 1 into a material with refractive index n 2, the refracted ray, the incident ray, and the normal to the interface between the materials all lie in the same plane. The angle of refraction θ 2 is related to the angle of incidence θ 1 by: n 1 sin θ 1 = n 2 sin θ 2

(a) When light travels from a higher-index medium (water) into a lower-index medium (air), the refracted ray is bent away from the normal. (b) When the angle of incidence is equal to the critical angle θ c, the angle of refraction is 90°. (c) If is greater than θ 1, there is no refracted ray, and total internal reflection occurs.

(a) Light can travel with little loss in a curved optical fiber, because the light is totally reflected whenever it strikes the core–cladding interface and because the absorption of light by the core itself is small. (b) Light being transmitted by a bundle of optical fibers. (PhotoDisc, Inc./Getty Images)

A doctor is using an endoscope to collect samples of tissue and fluid from the lung of a patient who has a history of asthma and allergies. Subsequently, the samples are examined under a microscope to obtain a diagnosis. (James King-Holmes/SPL/Photo Researchers, Inc.)