2220.3 Wave Interference

1. Diagram: 2. 4 blocks 3. 2 blocks 4. 32 blocks 5. 4 blocks 6. 1 wavelength 7. 8 wavelengths

8. A portion of the table and a graphic of the new wave are shown below. The values for the third column of the table are found by added the heights for wave 1 and wave 2.

Question 8 (con’t)

9. The new wave looks like the second wave, but it vibrates about the position of the first wave, rather than about the zero line. 21.1 Decibel Scale 1. Twice as loud. 2. 55 dB 3. Answers are: a. 80 dB b. 60 dB

4. Four times louder 5. Answers are:

a. 30 dB b. 50 dB c. 70 dB

Unit 8 Skill and Practice Sheets

22.1 Light Intensity Problems

1. Example problem: 4.8 W/m2 2. 0.0478 W/m2

3. 0.0119 W/m2

4. If distance from a light source doubles, then light intensity decreases by a factor of 4. Example: 4 × 0.0119 W/m2 approximately equals 0.0478 W/m2 (see questions 2 and 3). 5. Answers are:

a. 0.005 W/m2 b. 0.05 W/m2 c. 0.5 W/m2 d. 5 W/m2

6. The watts of a light source and light intensity are directly related. This means that if you use a light source that has 10 times the wattage, then light intensity will increase 10 times.

23.1 The Law of Reflection

1. Diagram at right: 2. The angle of reflection will

be 20 degrees.

3. Each angle will measure 45 degrees. x (blocks) Height wave 1 (blocks) Height wave 2 (blocks) Height of wave 1 +2 (blocks) 0 0 0 0 1 0.8 2 2.8 2 1.5 0 1.5 3 2.2 -2 0.2 4 2.8 0 2.8 5 3.3 2 5.3 6 3.7 0 3.7 7 3.9 -2 -1.9 8 4 0 4

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4. Diagram at right: 5. The angle is 96 degrees. There for the angles of incidence and reflection will each be 48 degrees.

6. The angles of incidence and reflection at point A are each 68.5 degrees; the angles of incidence and reflection at point B are each 21 degrees.

23.3 Refraction

Practice set 1:

1. The index of refraction will never be less than one because that would require the speed of light in a material to be faster than the speed of light in a vacuum. Nothing in the universe travels faster than that.

2. The index of refraction for air is less than that of glass because a gas like air is so much less dense than a solid like glass. The light rays are slowed each time they bump into an atom or molecule because they are absorbed and re-emitted by the particle. A light ray in a solid bumps into many more particles than a light ray traveling through a gas.

3. water: 2.26 × 108_{; glass: 2.0 × 10}8_{; diamond; 1.24 × 10}8 4. speed up

5. slow down

Practice set 2:

6. The light ray is moving from low-n to high-n so it will bend toward the normal.

7. The light ray is moving from high-n to low-n so it will bend away from the normal.

8. The difference in n from diamond to water is 1.09 while the difference from sapphire to air is 0.770. The ray traveling from diamond to water experiences the greater change in n so it would bend more.

9. From left to right, material B is water, emerald, helium, cubic zirconia.

23.3 Ray Diagrams

Practice set 1:

1. A is the correct answer. Light travels in straight lines and reflects off objects in all directions. This is why you can see something from different angles.

2. C is the correct answer. In this diagram, when light goes from air to glass it bends about 13 degrees from the path of the light ray in air. The light bends toward the normal to the air-glass surface because air has a lower index of refraction compared to glass. When the light re-enters the air, it bends about 13 degrees away for the light path in the glass and away from the normal.

As a ray of light approaches glass at an angle, it bends (refracts) toward the normal. As it leaves the glass, it bends away from the normal. However, if a ray of light enters a piece of glass perpendicular to the glass surface, the light ray will slow, but not bend because it is already in line with the normal. This happens because the index of refraction for air is lower than the index of refraction for glass. The index of refraction is a ratio that tells you how much light is slowed when it passes through a certain material.

3. A is the correct answer. Light rays that approach the lens that are in line with a normal to the surface pass right through, slowing but not bending. This is what happens at the principal axis. However, due to the curvature of the lens, the parallel light rays above and below the principal axis, hit the lens surface at an angle. These rays bend toward the normal (this bending occurs toward the fat part of the lens) and are focused at the lens’ focal point. The rays cross past the focal point. 4. Diagram:

Practice 2:

1. Diagram:

2. Diagram:

3. A lens acts like a magnifying glass if an object is placed to the left of a converging lens at a distance less than the focal length. The lens bends the rays so that they appear to be coming from a larger, more distant object than the real object. These rays you see form a virtual image. The image is virtual because the rays appear to come from an image, but don’t actually meet.

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24.1 The Electromagnetic Spectrum

1. Green 2. Green 3. 400× 10–9 m 4. 517× 1012 Hz 5. 652× 10–9 m 6. 566× 1012 Hz 7. The answer is: 8. λ = 0.122 meter 9. λ = 3.3 meters 10. f = 6 × 1016 _Hz 11. 1.0 × 1015 _Hz 12. 1.0 × 10-4 _Hz 13. Answers are: a. f =3 × 1019 hertz

b. It is the minimum frequency.

14. radio waves, microwaves, infrared, visible, ultraviolet, X rays, and gamma rays

15. gamma rays, X rays, ultraviolet, visible, infrared, microwaves, and radio waves

24.1 Doppler Shift

1. Answers are: a. 20 nm

b. 5.6 x 106 m/sec

c. The star is moving away from Earth. 2. Answers are:

a. 16 nm

b. 8.6 x 106 m/sec

c. The star is moving toward Earth.

3. Galaxy B is moving fastest because it has shifted farther toward the red (15 nm) than Galaxy A (9 nm).

4. It supports the Big Bang. This theory states that the universe began from a single point and has been expanding ever since. 5. Diagram at right: 6. Answers are: a. B and D b. A and C c. C d. B 7. Answers are: a. 10.5 nm b. longer c. 460.5 nm λ₁ λ₂ --- f₂ f₁ ---- =