Questions on corpuscles, waves and Young's fringes

Question 1

Give two reasons why Newton's corpuscular theory of light was preferred over Huygens' wave theory for over a century.

Accepted Answer

No convincing diffraction of light had been demonstrated, and shadows seemed perfectly sharp, consistent with particles in straight lines (1); and Newton's enormous scientific authority made his theory the default (1).

Question 2

Explain, in general terms, why bright and dark fringes appear in Young's double slit experiment.

Accepted Answer

Light spreading from the two slits overlaps on the screen. Where the two sets of waves arrive in step they reinforce, giving a bright fringe (1); where they arrive out of step they cancel, giving darkness (1).

Question 3

State what the constants ε₀ and μ₀ each describe.

Accepted Answer

ε₀, the permittivity of free space, relates to the electric field strength due to a charged object in free space (1); μ₀, the permeability of free space, relates to the magnetic flux density due to a current-carrying wire (1).

Question 4

State two behaviours of light that Newton's corpuscular theory and Huygens' wave theory could both explain.

Accepted Answer

Reflection (1) and refraction (1): both theories accounted for these, disagreeing only over the speed of light in the denser medium.

Question 5

State the nature of an electromagnetic wave.

Accepted Answer

Oscillating electric and magnetic fields at right angles to each other and to the direction of travel (1); the wave is self-propagating and needs no medium (1).

Question 6

Calculate the speed of electromagnetic waves predicted by Maxwell's formula c = 1/√(μ₀ε₀), using μ₀ = 4π × 10⁻⁷ H m⁻¹ and ε₀ = 8.85 × 10⁻¹² F m⁻¹, and state the significance of the result.

Accepted Answer

c = 1/√(μ₀ε₀) (1) c = 3.00 × 10⁸ m s⁻¹ (1) Equal to the measured speed of light, implying light is an electromagnetic wave (1)

Question 7

Hertz set up stationary radio waves with adjacent nodes 1.65 m apart, using an oscillator of frequency 9.1 × 10⁷ Hz. Calculate the wave speed and state what the result demonstrated.

Accepted Answer

Adjacent nodes are half a wavelength apart, so λ = 3.3 m (1) c = fλ = 3.0 × 10⁸ m s⁻¹ (1) Radio waves travel at the speed of light, confirming Maxwell's prediction (1)

Question 8

In Fizeau's experiment a wheel with 720 teeth first blocked the returning light at 12.6 revolutions per second, with the mirror 8.63 km away. Calculate the speed of light this gives.

Accepted Answer

First blocking: the wheel advances half a tooth, 1/1440 of a turn, during the round trip (1)
t = 1/(1440 × 12.6) = 5.51 × 10⁻⁵ s (1)
c = 2d/t = 2 × 8630/(5.51 × 10⁻⁵) (1)
c = 3.1 × 10⁸ m s⁻¹ (1)

Question 9

Explain why Young's fringes cannot be accounted for by a particle theory of light.

Accepted Answer

The dark fringes are places where light from one slit plus light from the other produces darkness (1). Streams of particles can only ever add together, giving more light (1); only waves arriving out of step can cancel, so the fringes demand a wave description (1).

Question 10

In a double slit experiment, light from the two slits arrives at a point on the screen with a path difference of 2.5 wavelengths. State and explain what is observed at this point.

Accepted Answer

A dark fringe (1): with a path difference of a whole number plus half a wavelength the waves arrive in antiphase, crest meeting trough, and cancel (1).

Question 11

The speed of light in free space is 3.00 × 10⁸ m s⁻¹ and μ₀ = 4π × 10⁻⁷ H m⁻¹. Use Maxwell's formula c = 1/√(μ₀ε₀) to determine a value for ε₀, the permittivity of free space.

Accepted Answer

Rearranging, ε₀ = 1/(μ₀c²) (1) = 1/(4π × 10⁻⁷ × (3.00 × 10⁸)²) (1) = 8.84 × 10⁻¹² F m⁻¹ (1).

Question 12

Measurements descended from Fizeau's method later compared the speed of light in air and in water. Explain why this comparison was decisive between the two theories of light.

Accepted Answer

Newton's corpuscular theory required light to travel faster in the denser medium to explain refraction towards the normal (1); Huygens' wave theory required it to travel slower (1). Light proved slower in water, so the wave theory's prediction was confirmed and the corpuscular account failed (1).

Question 13

Explain the significance of Hertz's experiments for the understanding of the electromagnetic spectrum.

Accepted Answer

Hertz generated previously unknown waves from purely electrical sparks (1), showed they reflect, refract and form stationary waves like light (1), and measured their speed as c. This confirmed Maxwell's electromagnetic theory directly (1), established that light belongs to a wider electromagnetic family, and opened the spectrum beyond the visible, radio first (1).

Question 14

Young published his double slit results in 1801, yet the wave theory was not generally accepted for decades. Suggest why.

Accepted Answer

Newton's reputation stood behind the corpuscular theory, and one experiment was not enough to overturn a century of consensus (1); acceptance came only as interference and diffraction evidence accumulated and the speed-in-water test went the wave theory's way (1).

Question 15

A physics society plans to repeat Fizeau's experiment with a wheel of 600 teeth and a mirror on a hillside 9.5 km away. Their motor can spin the wheel at up to 15 revolutions per second. Deduce whether they will be able to observe the first blocking of the returning light. c = 3.0 × 10⁸ m s⁻¹.

Accepted Answer

Round-trip time t = 2d/c = 2 × 9500/(3.0 × 10⁸) = 6.3 × 10⁻⁵ s (1). At the first blocking the wheel advances half a tooth spacing, 1/1200 of a turn, in this time (1). Rotation rate needed = (1/1200)/(6.3 × 10⁻⁵) = 13 rev s⁻¹ (1). This is below the motor's 15 rev s⁻¹, so the first blocking is just observable (1).

Question 16

In Fizeau's experiment the wheel's rotation rate is slowly increased beyond the first blocking, up to twice that rate. Explain what is seen at the eyepiece as this happens.

Accepted Answer

At the first blocking rate the wheel advances half a tooth spacing during the light's round trip, so the returning light lands on a tooth and the view is dark (1). At twice that rate the wheel advances a whole spacing in the same time (1), so the returning light passes through the next gap and the view brightens again (1).

Question 17

Light does in fact diffract, yet for over a century nobody demonstrated it convincingly and shadows appeared perfectly sharp. Suggest why the diffraction of light escaped detection, and explain why sharp shadows appeared to support Newton.

Accepted Answer

The wavelength of light is extremely small, of order 10⁻⁷ m (1), so its bending at everyday obstacles and edges is far too slight to notice and shadows look sharp (1). Sharp shadows are exactly what streams of particles travelling in straight lines predict, so the observations seemed to confirm the corpuscular theory (1).

Question 18

Describe Fizeau's determination of the speed of light, and explain how the speed is calculated from the measurements. State one reason the measurement was significant.

Accepted Answer

Light passes through a gap between the teeth of a rotating wheel, travels to a distant mirror several kilometres away and returns along the same path (1). The rotation rate is increased until the returning light is first blocked, when the wheel has advanced half a tooth spacing during the round trip (1). For N teeth rotating at f revolutions per second, the round-trip time is t = 1/(2Nf) (1), and c = 2d/t with d the measured distance to the mirror (1). Significance: the first accurate terrestrial measurement of c, making the speed of light a repeatable, checkable quantity, later compared against Maxwell's prediction (1).