# Electromagnetic waves in free space

1) Which of the following statements about electromagnetic waves in free space are true? (There could be more than one correct choice.)

A) The higher-frequency travel faster than the lower-frequency waves.

B) The higher-frequency waves have shorter wavelengths than the lower-frequency waves.

C) The wavelengths of the visible waves are some of the longest electromagnetic waves.

D) The wavelengths of the visible waves are some of the shortest electromagnetic waves.

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2) Which one of the following types of electromagnetic wave travels through space the fastest?

A) radio waves

B) infrared

C) ultraviolet

D) microwaves

E) They all travel through space at the same speed.

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3) For an electromagnetic wave in free space having an electric field of amplitude E and a magnetic field of amplitude B, the ratio of B/E is equal to

A) c

B) c2

C) 1/c

D) 1/c2

E)

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4) If the index of refraction of a material is 2, this means that light travels

A) 2 times as fast in air as it does in vacuum.

B) 2 times as fast in the material as it does in air.

C) 2 times as fast in vacuum as it does in the material.

D) 2 times as fast in the material than it does in vacuum.

E) 1/2 as fast in air as it does in the material.

5) Light goes from material having a refractive index of n1 into a material with refractive index n2. If the refracted light is bent away from the normal, what can you conclude about the indices of refraction?

A) n1 > n2

B) n1 ≥ n2

C) n1 < n2

D) n1 ≤ n2

E) n1 = n2

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6) The critical angle for a beam of light passing from water into air is 48.8°. This means that all light rays with an angle of incidence in the water that is greater than 48.8° will be

A) totally absorbed by the water.

B) totally reflected.

C) partially reflected and partially transmitted.

D) totally transmitted.

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7) If the lens in a person’s eye is too highly curved, this person is suffering from

A) farsightedness.

B) spherical aberration.

C) astigmatism.

D) chromatic aberration.

E) nearsightedness.

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8) A negative magnification for a mirror means that

A) the image is inverted, and the mirror could be either concave or convex.

B) the image is upright, and the mirror is convex.

C) the image is inverted, and the mirror is convex.

D) the image is inverted, and the mirror is concave.

E) the image is upright, and the mirror could be either concave or convex.

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9) Single concave spherical mirrors produce images that

A) are always smaller than the actual object.

B) are always larger than the actual object.

C) are always the same size as the actual object.

D) could be smaller than, larger than, or the same size as the actual object, depending on the placement of the object.

E) are always real.

10) The image formed by a single concave lens

A) is always real.

B) is always virtual.

C) could be real or virtual, depending on whether the object distance is smaller or greater than the focal length.

D) could be real or virtual, but is always real when the object is placed at the focal point.

E) is always inverted.

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11) A bar magnet is close to a solenoid, as shown in the figure. As viewed through the solenoid looking toward the magnet, what is the direction (clockwise or counterclockwise) of the current (if any) induced in the solenoid in each case?

(a) The magnet is pushed toward the solenoid.

(b) The magnet and solenoid both move to the right at 25 cm/s.

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12) The wire in the figure carries a current I that is increasing with time at a constant rate. The wire and the three loops are all in the same plane. What is true about the currents induced in each of the three loops shown?

A) No current is induced in any loop.

B) The currents are counterclockwise in all three loops.

C) The currents are clockwise in all three loops.

D) Loop A has clockwise current, loop B has no induced current, and loop C has counterclockwise current.

E) Loop A has counterclockwise current, loop B has no induced current, and loop C has clockwise current.

13) As shown in the figure, a battery supplies a steady current to the solenoid on the left. The two solenoids are moving toward each other with speeds v. The direction of the induced current through the resistor R is

A) from a to b.

B) from b to a.

C) No current is induced.

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14) What is the maximum value of the magnetic field at a distance of 2.5 m from a light bulb that radiates 100 W of single-frequency sinusoidal electromagnetic waves uniformly in all directions? (ε0 = 8.85 × 10-12 C2/N ∙ m2, μ0 = 4π × 10-7 T ∙ m/A, c = 3.0 × 108 m/s)

A) 0.10 μT

B) 0.40 μT

C) 0.50 μT

D) 0.60 μT

E) 0.80 μT

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15) The frequency of a microwave signal is 9.76 GHz. What is its wavelength? (c = 3.00 × 108 m/s)

A) 3.07 cm

B) 2.07 cm

C) 1.07 cm

D) 5.07 cm

E) 4.07 cm

I. Solve the following problems and Show your work.

1) A radio station broadcasts at a wavelength of 600 nm. How far from the transmitter will this signal travel in 67 m sec? (c = 3.0 × 108 m/s). (1.5 points)

2) One converging lens and a convex mirror are separated by 1.00 m along the same principal axis, as shown in the figure. The magnitude of the focal length of the converging lens is 25 cm, while the magnitude of the focal length of the convex mirror is 40 cm. An object 8.25 cm tall is placed 35 cm to the left of the converging lens.

(a) Where is the final image produced by this combination of lenses?

(Give your answer relative to the diverging lens.)

(b) Draw the beams to locate the location of final Image

(c) Find total magnifications. Is final image real or virtual? Right side up or upside down?

(3 points)

3) 39) A tank holds a layer of oil, of thickness To = 1.65 m, that floats on a layer of syrup of thickness Ts = 0.830 m, as shown in the figure. Both liquids are clear and do not mix together. A light ray, originating at the bottom of the tank at point P, crosses the oil-syrup interface at a point 0.900 m from the axis. The ray continues and arrives at the oil-air interface, 2.00 m to the right of P and at the critical angle. What is the index of refraction of the syrup? (3 points)

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