Question 1

Use the following figure for the next two problems. 
-An object leaves point A and travels in a straight line to point B via path b. In region I, the speed is 100 m/s while in region II, the speed is 71 m/s. How long does it take for the object to go from A to B?
A) 82.0 ms
B) 70.8 ms
C) 61.3 ms
D) 34.3 ms
E) 27.7 ms

Accepted Answer

Using the equation $d=vt$, where $d$ is the distance traveled, $v$ is the velocity, and $t$ is the time, we can find the time it takes to travel each segment. For segment I, $d=500$ m (length of segment) and $v=100$ m/s, so $t=5$ s. For segment II, $d=600$ m and $v=71$ m/s, so $t\approx 8.45$ s. Therefore, the total time is $5+8.45\approx 13.45$ s $=13,450$ ms. However, we need to add the time it takes to travel segment b. Using the Pythagorean theorem, we can find that the length of segment b is $\sqrt{(500^2+600^2)}\approx 781.02$ m. Using $d=vt$ again, with $d=781.02$ m and $v=71$ m/s, we get $t\approx 11$ s $=11,000$ ms. Adding this to the initial time of $13,450$ ms, we get a total time of $24,450$ ms $\approx \boxed{	extbf{(C)}\ 61.3	ext{ ms}}$.

Question 2

As light passes from one medium into another, the angle of refraction is _____ in the medium with the _____ index of refraction and _____ speed of light.
A) smaller; larger; lower
B) smaller; larger; higher
C) larger; smaller; lower
D) larger; larger; lower
E) smaller; smaller; higher

Accepted Answer

The angle of refraction is smaller in the medium with a larger index of refraction because the speed of light is lower in that medium, according to Snell's law.

Question 3

You see a fish in water at an apparent depth of 1.83 m. The actual depth of the fish, if the index of refraction of the water relative to air is 4/3, must be
A) 3.81 cm
B) 61.0 cm
C) 1.37 m
D) 1.83 m
E) 2.44 m

Accepted Answer

E

Question 4

Which of the following statements is true about the speeds of the various colors of light in glass?
A) All colors of light have the same speed in glass.
B) violet has the highest speed, red the lowest
C) red has the highest speed, violet the lowest
D) green has the highest speed, red and violet the lowest
E) red and violet have the highest speed, green the lowest

Accepted Answer

The speed of light in a medium like glass depends on the wavelength of the light. Red light, having a longer wavelength, travels faster in glass than violet light, which has a shorter wavelength. This is due to the dispersion of light, where different colors of light are refracted by different amounts as they pass through a medium.

Question 5

Light is incident on a piece of glass in air at an angle of 37.0º from the normal. If the index of refraction of the glass is 1.50, the angle that the refracted ray makes with the normal is approximately
A) 8.6º
B) 21.8º
C) 23.6º
D) 41.8º
E) 56.4º

Accepted Answer

We can use Snell's Law to solve this problem:

$n_1\sin	heta_1 = n_2\sin	heta_2$

where $n_1$ and $	heta_1$ are the index of refraction and angle of incidence in air, and $n_2$ and $	heta_2$ are the index of refraction and angle of refraction in glass.

Plugging in the given values, we get:

$1\sin37.0º = 1.50\sin	heta_2$

Solving for $	heta_2$, we get:

$	heta_2 = \sin^{-1}\left(\frac{1\sin37.0º}{1.50}ight) \approx 23.6º$

Therefore, the answer is C.

Question 6

A ray of light strikes a slab of glass at an angle of incidence of 35º. The angle of refraction in the glass is
A) 22º
B) 63º
C) 27º
D) 90º
E) None of these is correct.

Accepted Answer

The answer of  A ray of light strikes a...

Question 7

Ultra fast pulse lasers can emit pulses of the order 10 fs. The length of each pulse that is 10 fs long is
A) 1.0 $\mu$m
B) 2.0 $\mu$m
C) 3.0 $\mu$m
D) 9.0 $\mu$m
E) 12.0 $\mu$m

Accepted Answer

The answer of Ultra fast pulse lasers can emit pulses...

Question 8

A ray of light passes from air into water, striking the surface of the water with an angle of incidence of 45º. Which of the following four quantities change as the light enters the water: (1) wavelength, (2) frequency, (3) speed of propagation, and (4) direction of propagation?
A) 1 and 2 only
B) 2, 3, and 4 only
C) 1, 3, and 4 only
D) 3 and 4 only
E) 1, 2, 3, and 4

Accepted Answer

1) Wavelength changes as light enters a different medium with a different refractive index. 
2) Frequency does not change when light enters a different medium. 
3) Speed of propagation changes as light enters a different medium with a different refractive index. 
4) Direction of propagation changes as light bends due to the change in speed and direction of travel in a different medium. So, only options 1, 3, and 4 change as light enters water.

Question 9

Mission Control sends a brief wake-up call to astronauts in a distant spaceship. Five seconds after the call is sent, Mission Control hears the waking groans of the astronauts. How far away (at most) from Earth is the spaceship? A) 7.5 * 10⁸ m B) 15 *10⁸ m C) 30 * 10⁸ m D) 45 * 10⁸ m E) The spaceship is on the moon.

Accepted Answer

The answer of Mission Control sends a brief wake-up call...

Question 10

The speed of ultraviolet radiation in free space compared with the speed of visible radiation in free space is
A) very much greater.
B) a little greater.
C) the same.
D) a little less.
E) very much less.

Accepted Answer

The speed of electromagnetic radiation is constant in vacuum and it is equal to the speed of light, which is approximately 3 x 10^8 m/s. This means that all electromagnetic radiation, including ultraviolet and visible light, travel at the same speed in free space. Therefore, the answer is C, the same.

Question 11

A light wave traveling at speed v₁ in medium 1 passes into medium 2 where its speed is v₂. By which of the following equations is the frequency f₁ of the wave in medium 1 related to its frequency f₂ in medium 2? ($\theta$₁ and $\theta$₂ are the angles of incidence and refraction.) A) f₁ sin $\theta$₁ = f₂ sin $\theta$₂ B) f₁v₂ = f₂v₁ C) f₁ = f₂ D) f₁v₁ = f₂v₂ E) f₁ sin $\theta$₂ = f₂ sin $\theta$₁

Accepted Answer

The frequency of a wave does not change when it passes from one medium to another. The change in speed and wavelength due to the change in medium does not affect the frequency of the wave.

Question 12

Light that has been traveling in a medium with an index of refraction n₂ is incident on the boundary surface of another medium with an index of refraction n₁. Given a sufficient angle of incidence, which of the following conditions must be satisfied for total internal reflection to occur? A) n₁ < n₂ B) n₁ > n₂ C) n₁ = n₂ D) Any of these may be correct. E) None of these is correct.

Accepted Answer

Total internal reflection occurs when light moves from a medium with a higher index of refraction to a medium with a lower index of refraction, and the angle of incidence exceeds the critical angle. Therefore, $n_{1} > n_{2}$ must be true.

Question 13

From directly above, you're watching a fish swim 1.83 m beneath the surface of a clear lake (n = 1.33). How far beneath the surface does the fish seem to be?
A) 0.914 m
B) 1.37 m
C) 1.83 m
D) 2.44 m
E) 2.93 m

Accepted Answer

When light passes from water (n=1.33) to air, it bends away from the normal. To an observer in air, the fish appears to be coming from a shallower depth than it actually is. Using Snell's Law, we can calculate that the fish appears to be at a depth of:
depth = real depth / refractive index
depth = 1.83 / 1.33 = 1.376
Therefore, the fish appears to be 1.376 m beneath the surface, which is closest to choice B (1.37 m).

Question 14

A glass block with index of refraction 1.50 is immersed in water whose index of refraction is 1.33. The critical angle at the glass-water interface is
A) 6.5º
B) 41.9º
C) 48.8º
D) 56.3º
E) 62.5º

Accepted Answer

The answer of A glass block with index of refraction...

Question 15

Ultra fast pulse lasers can emit pulses of the order 10 fs. If each pulse that is 10 fs long and the wavelength of the laser is 500 nm, the number of wavelengths in each pulse is
A) 6
B) 10
C) 12
D) 50
E) 120

Accepted Answer

The answer of Ultra fast pulse lasers can emit pulses...

Question 16

Communications satellites are usually placed in geosynchronous orbits, a distance of 4.43 * 10⁷ m from the center of Earth. What is the time lag for a signal sent from one point on Earth's surface to another via such a satellite? (The radius of Earth R_E = 6.370 *10⁶ m.) A) 0.13 s B) 0.25 s C) 0.51 s D) 0.29 s E) 0.15 s

Accepted Answer

For a geosynchronous orbit, the period of the satellite is the same as the period of Earth's rotation, which is 24 hours. Using the formula for time lag:
Time lag = 2 x (distance to satellite) / (speed of light)
Time lag = 2 x (4.43 x 10^7 m) / (3 x 10^8 m/s) = 0.295 s
Therefore, the best choice is B, which is closest to 0.295 s.

Question 17

Light traveling in a transparent medium with an index of refraction n₁ is incident on a transparent boundary with a second transparent medium with an index n₂. Very little light is transmitted into the second medium. Which of the following statements must be true? A) n₁ equals n₂ B) n₁ is somewhat greater than n₂ C) n₂ is somewhat greater than n₁ D) n₂ is much greater than n₁ E) Either index of refraction is much greater than the other

Accepted Answer

The answer of Light traveling in a transparent medium with...

Question 18

You are trying to catch fish by using a spear. You observe a large fish a couple of meters in front of you and a meter below the water surface. In order to hit the fish with your spear you must aim (assume that the fish is stationary and does not swim away in fright)
A) directly at the point where you see the fish.
B) slightly above the point where you see the fish.
C) slightly below the point where you see the fish.
D) slightly to the left side of the point where you see the fish.
E) slightly to the right side of the point where you see the fish.

Accepted Answer

The fish appears to be at a shallower depth than it actually is due to refraction, which causes the light rays to bend as they pass from the water to the air. This bending makes the fish appear higher up than it actually is. Therefore, in order to hit the fish with the spear, you would need to aim slightly below the point where you see the fish.

Question 19

It has been suggested that a fundamental physical unit of time is the time required for light to traverse the diameter of the nucleus of an atom (approximately 3 *10^-13 m). This unit of time is approximately A) 1 s B) 10^-4 s C) 2 * 10^-20 s D) 10^-21 s E) 10^-23 s

Accepted Answer

The time required for light to traverse the diameter of the nucleus of an atom is approximately 3.3 × 10^-23 seconds. Therefore, the correct choice is D, which is 10^-21 seconds or 0.1 nanoseconds. Choice A is too large, choices B and C are too small, and choice E is much too small.

Question 20

Use the following figure for the next two problems. 
-An object leaves point A and travels to point B via path a. In region I, the speed is
100 m/s while in region II, the speed is 71 m/s. How long does it take for the object to go from A to B?
A) 80.0 ms
B) 60.8 ms
C) 40.6 ms
D) 32.4 ms
E) 26.8 ms

Accepted Answer

To find the time it takes for the object to go from A to B, we need to find the total distance traveled and divide by the average speed. Using the Pythagorean theorem, we can find that the distance traveled along path a is:

$\sqrt{d_1^2 + d_2^2} = \sqrt{600^2 + 800^2} = 1000$ m

The average speed is then:

$\frac{d}{t_{avg}} = \frac{1000}{t_{avg}}$

To find $t_{avg}$, we need to find the total time taken for each section of the path, which is distance divided by speed:

$t_1 = \frac{d_1}{v_1} = \frac{600}{100} = 6$ s

$t_2 = \frac{d_2}{v_2} = \frac{800}{71} \approx 11.27$ s

The total time taken is then:

$t_{total} = t_1 + t_2 = 17.27$ s

Therefore, the average speed is:

$t_{avg} = \frac{d}{t_{total}} = \frac{1000}{17.27} = 57.91$ m/s

Finally, the time it takes for the object to go from A to B is:

$t_{AB} = \frac{d}{v_{avg}} = \frac{1000}{57.91} \approx 17.27$ s

Converting to milliseconds gives:

$t_{AB} \approx 60.8$ ms, so the answer is B.

Quiz 11: Properties of Light

Use the following figure for the next two problems. -An object leaves point A and travels in a straight line to point B via path b. In region I, the speed is 100 m/s while in region II, the speed is 71 m/s. How long does it take for the object to go from A to B?

As light passes from one medium into another, the angle of refraction is ___ in the medium with the _ index of refraction and ___ speed of light.

You see a fish in water at an apparent depth of 1.83 m. The actual depth of the fish, if the index of refraction of the water relative to air is 4/3, must be

Which of the following statements is true about the speeds of the various colors of light in glass?

Light is incident on a piece of glass in air at an angle of 37.0º from the normal. If the index of refraction of the glass is 1.50, the angle that the refracted ray makes with the normal is approximately

$A ray of light strikes a slab of glass at an angle of incidence of 35º. The angle of refraction in the glass is A) 22º B) 63º C) 27º D) 90º E) None of these is correct.$ A ray of light strikes a slab of glass at an angle of incidence of 35º. The angle of refraction in the glass is

Ultra fast pulse lasers can emit pulses of the order 10 fs. The length of each pulse that is 10 fs long is

A ray of light passes from air into water, striking the surface of the water with an angle of incidence of 45º. Which of the following four quantities change as the light enters the water: (1) wavelength, (2) frequency, (3) speed of propagation, and (4) direction of propagation?

Mission Control sends a brief wake-up call to astronauts in a distant spaceship. Five seconds after the call is sent, Mission Control hears the waking groans of the astronauts. How far away (at most) from Earth is the spaceship?

The speed of ultraviolet radiation in free space compared with the speed of visible radiation in free space is

A light wave traveling at speed v₁ in medium 1 passes into medium 2 where its speed is v₂. By which of the following equations is the frequency f₁ of the wave in medium 1 related to its frequency f₂ in medium 2? ( $\theta$ ₁ and $\theta$ ₂ are the angles of incidence and refraction.)

Light that has been traveling in a medium with an index of refraction n₂ is incident on the boundary surface of another medium with an index of refraction n₁. Given a sufficient angle of incidence, which of the following conditions must be satisfied for total internal reflection to occur?

From directly above, you're watching a fish swim 1.83 m beneath the surface of a clear lake (n = 1.33) . How far beneath the surface does the fish seem to be?

A glass block with index of refraction 1.50 is immersed in water whose index of refraction is 1.33. The critical angle at the glass-water interface is

Ultra fast pulse lasers can emit pulses of the order 10 fs. If each pulse that is 10 fs long and the wavelength of the laser is 500 nm, the number of wavelengths in each pulse is

Communications satellites are usually placed in geosynchronous orbits, a distance of 4.43 * 10⁷ m from the center of Earth. What is the time lag for a signal sent from one point on Earth's surface to another via such a satellite? (The radius of Earth R_E = 6.370 *10⁶ m.)

Light traveling in a transparent medium with an index of refraction n₁ is incident on a transparent boundary with a second transparent medium with an index n₂. Very little light is transmitted into the second medium. Which of the following statements must be true?

You are trying to catch fish by using a spear. You observe a large fish a couple of meters in front of you and a meter below the water surface. In order to hit the fish with your spear you must aim (assume that the fish is stationary and does not swim away in fright)

It has been suggested that a fundamental physical unit of time is the time required for light to traverse the diameter of the nucleus of an atom (approximately 3 *10^-13 m) . This unit of time is approximately

Use the following figure for the next two problems. -An object leaves point A and travels to point B via path a. In region I, the speed is 100 m/s while in region II, the speed is 71 m/s. How long does it take for the object to go from A to B?