Chapter 24 & 26. Electromagnetic Waves & Wave Properties. 1. A wave is a traveling disturbance. 2. A wave carries energy from place to place.

Transcription

1 Chapter 4 & 6 Electromagnetic Waes & Wae Properties DR JJ UiTM-Cutnell & Johnson 7th ed. 6. The Nature of Waes. A wae is a traeling disturbance.. A wae carries energy from place to place. Waes trael to the right Waes trael to the left x x y Asin πf t Asinω t λ f λ x x y Asin πf t + Asinω t + λ f λ DR JJ UiTM-Cutnell & Johnson 7th ed. DR JJ UiTM-Cutnell & Johnson 7th ed.

2 6. Periodic Waes y A sin ω t Transerse wae Disturbance ertical direction Wae moe right or left Mathematical description of a traeling wae x x A sin ω t fλ Where is the wae speed Longitudinal wae Disturbance & wae moe in the same direction fλ DR JJ UiTM-Cutnell & Johnson 7th ed Periodic Waes In the drawing, one cycle is shaded in color. The amplitude A is the maximum ertical displacement from the particles undisturbed position. The waelength is the horizontal length of one cycle of the wae.. The period is the time taken for one complete cycle. The frequency is the number of cycles in a second in units of Hz, or s- f T DR JJ UiTM-Cutnell & Johnson 7th ed. 4 DR JJ UiTM-Cutnell & Johnson 7th ed.

3 6. Periodic Waes Example The Waelengths of Radio Waes AM and FM radio waes are transerse waes consisting of electric and magnetic field disturbances traeling at a speed of 3.00x0 m/s. A station broadcasts AM radio waes whose frequency is 30x0 3 Hz and an FM radio wae whose frequency is 9.9x0 6 Hz. Find the distance between adjacent crests in each wae. AM λ T f λ fλ λ m s Hz f 44 m FM f λ m s Hz 3.6 m DR JJ UiTM-Cutnell & Johnson 7th ed The Electromagnetic Spectrum Conceptual Example The Diffraction of AM and FM Radio Waes Diffraction is the ability of a wae to bend around an obstacle or the edges of an opening. Would you expect AM or FM radio waes to bend more readily around an obstacle such as a building? DR JJ UiTM-Cutnell & Johnson 7th ed. 6 DR JJ UiTM-Cutnell & Johnson 7th ed. 3

4 4. The Nature of Electromagnetic Waes Two straight wires connected to the terminals of an AC generator can create an electromagnetic wae. Only the electric wae traeling to the right is shown here. DR JJ UiTM-Cutnell & Johnson 7th ed The Nature of Electromagnetic Waes The current used to generate the electric wae creates a magnetic field. DR JJ UiTM-Cutnell & Johnson 7th ed. DR JJ UiTM-Cutnell & Johnson 7th ed. 4

5 4. The Nature of Electromagnetic Waes This picture shows the wae of the radiation field far from the antenna. The speed of an electromagnetic wae in a acuum is: c m s DR JJ UiTM-Cutnell & Johnson 7th ed The Nature of Electromagnetic Waes A radio wae can be detected with a receiing antenna wire that is parallel to the electric field. DR JJ UiTM-Cutnell & Johnson 7th ed. 0 DR JJ UiTM-Cutnell & Johnson 7th ed. 5

6 4. The Nature of Electromagnetic Waes With a receiing antenna in the form of a loop, the magnetic field of a radio wae can be detected. DR JJ UiTM-Cutnell & Johnson 7th ed. 4. The Electromagnetic Spectrum c Like all waes, electromagnetic waes in accum hae a waelength and frequency, related by: In other medium, the speed fλ is less than in acuum. ( < c), fλ ε µ but the frequency remains the 0 0 same DR JJ UiTM-Cutnell & Johnson 7th ed. DR JJ UiTM-Cutnell & Johnson 7th ed. 6

7 4. The Electromagnetic Spectrum Example The Waelength of Visible Light Find the range in waelengths for isible light in the frequency range between 4.0x0 4 Hz and 7.9x0 4 Hz. λ c f m s Hz m 750 nm λ c f m s 3. 0 Hz m 30 nm DR JJ UiTM-Cutnell & Johnson 7th ed The Speed of Light The speed of light in a acuum c m s Maxwell s prediction of the speed of light c m s ε µ o o 7 (.5 0 C ( N m ))( 4π 0 T m A) DR JJ UiTM-Cutnell & Johnson 7th ed. 4 DR JJ UiTM-Cutnell & Johnson 7th ed. 7

8 4.4 The Energy Carried by Electromagnetic Waes Electromagnetic waes, like water waes, carry energy. DR JJ UiTM-Cutnell & Johnson 7th ed The Energy Carried by Electromagnetic Waes The total energy density carried by an electromagnetic wae u Total energy Volume But u E u B ; So, total u is; Hence So Since E & B are sinusoidal u E + u B ε oe + B µ ε oe B µ o u ε oe + ε oe ε oe B µ o E B c B or E cb ε oµ o E c 3 0 m / s B ε 0µ 0 E B 0 Erms 0 Brms DR JJ UiTM-Cutnell & Johnson 7th ed. 6 o DR JJ UiTM-Cutnell & Johnson 7th ed.

9 4.4 The Energy Carried by Electromagnetic Waes S P Total energy ucta cu A t A ta DR JJ UiTM-Cutnell & Johnson 7th ed. 7 Chapter 6 Index of Refraction DR JJ UiTM-Cutnell & Johnson 7th ed. DR JJ UiTM-Cutnell & Johnson 7th ed. 9

10 6. The Index of Refraction Light traels through a acuum at a speed c m s Light traels through materials at a speed less than its speed in a acuum. DEFINITION OF THE INDEX OF REFRACTION The index of refraction of a material is the ratio of the speed of light in a acuum to the speed of light in the material: c Speed of light in acuum n Speed of light in the material In other medium, the speed fλ is less than in acuum. ( < c), fλ ε µ 0 0 c but the frequency remains the same DR JJ UiTM-Cutnell & Johnson 7th ed The Index of Refraction DR JJ UiTM-Cutnell & Johnson 7th ed. 0 DR JJ UiTM-Cutnell & Johnson 7th ed. 0

11 6. Snell s Law and the Refraction of Light SNELL S LAW Light wae bend (direction change) when entering medium of different index of refraction SNELL S LAW OF REFRACTION When light traels from a material with one index of refraction to a material with a different index of refraction, the angle of incidence is related to the angle of refraction by n sinθ n sin θ DR JJ UiTM-Cutnell & Johnson 7th ed. 6. Snell s Law and the Refraction of Light THE DERIVATION OF SNELL S LAW Taking ratios λ λ sin θ ; sin θ ; h h But sin θ λ λ sin θ λ h λ h λ c ; fλ ; n f c DR JJ UiTM-Cutnell & Johnson 7th ed. DR JJ UiTM-Cutnell & Johnson 7th ed.

12 6. Snell s Law and the Refraction of Light THE DERIVATION OF SNELL S LAW sin θ sin θ λ λ h h / / f f So, c / n c / n n n n sinθ n sin θ DR JJ UiTM-Cutnell & Johnson 7th ed Snell s Law and the Refraction of Light Example Determining the Angle of Refraction A light ray strikes an air/water surface at an angle of 46 degrees with respect to the normal. Find the angle of refraction when the direction of the ray is (a) from air to water and (b) from water to air. DR JJ UiTM-Cutnell & Johnson 7th ed. 4 DR JJ UiTM-Cutnell & Johnson 7th ed.

13 6. Snell s Law and the Refraction of Light (a) n sinθ sinθ n (.00) sin θ 33 (b) n sinθ sinθ n (.33) sin θ 74 DR JJ UiTM-Cutnell & Johnson 7th ed Snell s Law and the Refraction of Light APPARENT DEPTH Example Finding a Sunken Chest The searchlight on a yacht is being used to illuminate a sunken chest. At what angle of incidence should the light be aimed? DR JJ UiTM-Cutnell & Johnson 7th ed. 6 DR JJ UiTM-Cutnell & Johnson 7th ed. 3

14 6. Snell s Law and the Refraction of Light (.0 3.3) 3 θ tan n sinθ sinθ n (.33) sin θ 44 DR JJ UiTM-Cutnell & Johnson 7th ed Snell s Law and the Refraction of Light Apparent depth, obserer directly aboe object n d d n DR JJ UiTM-Cutnell & Johnson 7th ed. DR JJ UiTM-Cutnell & Johnson 7th ed. 4