Figure 2 shows the apparatus Fizeau used to determine the speed of light. The following observations are made. A: When the speed of rotation is low the observer sees the light returning after reflection by the mirror M. B: When the speed of the wheel is slowly increased the observer continues to see the light until the wheel reaches a certain speed. At this speed the observer cannot see the light. Table 1 shows data from Fizeau's experiment at the instant when observation B is made. Distance from M to W: 8.6 km Number of wheel revolutions per second: 12 Number of teeth in the wheel: 720 It can be shown that the speed of light is given by the equation $c = 4d f n$ Discuss whether the data in Table 1 are consistent with the accepted value for the speed of light. The speed of the wheel is further increased. Deduce the value of $v$ when the observer would next be unable to see light returning from the mirror. Explain how the nature of light is implied by Maxwell's theory of electromagnetic waves and Fizeau's result.

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Figure 2 shows the apparatus Fizeau used to determine the speed of light - AQA - A-Level Physics - Question 2 - 2017 - Paper 7

Question 2

Figure 2 shows the apparatus Fizeau used to determine the speed of light. The following observations are made. A: When the speed of rotation is low the observer se... show full transcript

Worked Solution & Example Answer:Figure 2 shows the apparatus Fizeau used to determine the speed of light - AQA - A-Level Physics - Question 2 - 2017 - Paper 7

Step 1

Explain these observations.

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Answer

Observation A

When the speed of rotation is low, the light from the source reflects off the mirror M and returns back to the observer O. The light is visible to the observer because it travels slowly compared to the rate of rotation of the toothed wheel W. In this scenario, the wheel does not block the returning light, allowing the observer to see it clearly.

Observation B

As the speed of the wheel increases, a point is reached where the teeth of the wheel begin to block the path of the returning light. The observer continues to see the light until the wheel's rotational speed matches the light's travel time. At this critical speed, the light is blocked by the next tooth in the wheel before it can return to the observer, rendering it invisible.

Step 2

Discuss whether the data in Table 1 are consistent with the accepted value for the speed of light.

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Answer

To find the speed of light using Table 1 data, we utilize the formula:

$c = 4dnf$

Given values from the table:

Distance $d = 8.6 ext{ km} = 8600 ext{ m}$
Number of wheel revolutions per second $f = 12 ext{ Hz}$
Number of teeth in the wheel $n = 720$

Substituting these values into the equation:

$c = 4 imes 8600 imes 12 imes 720$

Calculating this gives:

$c = 4 imes 8600 imes 12 imes 720 = 2.97 imes 10^8 ext{ m/s}$

This result is consistent with the accepted value for the speed of light, which is approximately $3.00 imes 10^8 ext{ m/s}$ . Thus, the data support the conclusion that Fizeau's experiment provides a reliable estimate of the speed of light.

Step 3

Deduce the value of $v$ when the observer would next be unable to see light returning from the mirror.

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Answer

As the speed of the wheel increases further, the next point where the observer cannot see light returning occurs when the wheel rotates fast enough for the next tooth to block the reflected light. The relationship between the speed of light $c$ , the distance d, and the rotational speed can be expressed as:

$v = rac{1}{2} imes rac{c}{n}$

Using the previously calculated value of $c = 2.97 imes 10^8 ext{ m/s}$ and considering that there are 720 teeth in the wheel, the observer will next be unable to see the light when:

= 2.06 imes 10^5 ext{ m/s}$$

Step 4

Explain how the nature of light is implied by Maxwell's theory of electromagnetic waves and Fizeau's result.

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Answer

Maxwell's theory of electromagnetic waves predicted a value for the speed of electromagnetic waves as $c = 3.00 imes 10^8 ext{ m/s}$ . Fizeau's experimental results yielded a speed of light that closely matched this prediction, thereby supporting the theory.

This alignment implies that light behaves not merely as a particle but as an electromagnetic wave. Fizeau's findings underscored the wave nature of light by demonstrating that it could be modulated and quantified through its interaction with a rotating apparatus, further corroborating Maxwell’s theories.

Figure 2 shows the apparatus Fizeau used to determine the speed of light - AQA - A-Level Physics - Question 2 - 2017 - Paper 7

Worked Solution & Example Answer:Figure 2 shows the apparatus Fizeau used to determine the speed of light - AQA - A-Level Physics - Question 2 - 2017 - Paper 7

Explain these observations.

Observation A

Observation B

Discuss whether the data in Table 1 are consistent with the accepted value for the speed of light.

Deduce the value of $v$ when the observer would next be unable to see light returning from the mirror.

Explain how the nature of light is implied by Maxwell's theory of electromagnetic waves and Fizeau's result.

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