Worksheet: Coherent Light

In this worksheet, we will practice determining whether two or more electromagnetic waves will interfere to form coherent or incoherent light.

Q1:

Which of the following statements correctly defines what is meant by the term β€œcoherent light”?

  • ATwo or more light waves are coherent if they have the same frequency and a constant phase difference.
  • BTwo or more light waves are coherent if they have the same amplitude and a constant phase difference.
  • CTwo or more light waves are coherent if they have a constant phase difference.
  • DTwo or more light waves are coherent if they have the same frequency.
  • ETwo or more light waves are coherent if they have the same frequency and amplitude.

Q2:

Which of the following statements correctly defines what is meant by incoherent light?

  • ATwo or more light waves are incoherent if they have the same frequency and constant phase differences.
  • BTwo or more light waves are incoherent if they have different frequencies or nonconstant phase differences.
  • CTwo or more light waves are incoherent if they have both different frequencies and different amplitudes.
  • DTwo or more light waves are incoherent if they have both different amplitudes and nonconstant phase differences.
  • ETwo or more light waves are incoherent if they have different amplitudes.

Q3:

In each of the following diagrams, five light waves are shown. Which of the diagrams shows coherent light?

  • A
  • B
  • C
  • D
  • E

Q4:

The figure shows five light waves. Which light wave is not coherent with the other four?

  • Aiv
  • Biii
  • Cv
  • Dii
  • Ei

Q5:

The figure shows five light waves. Which light wave is not coherent with the other four?

  • Av
  • Biii
  • Civ
  • Dii
  • Ei

Q6:

In each of the following diagrams, five light waves are shown. Which of the diagrams shows incoherent light?

  • A
  • B
  • C
  • D
  • E

Q7:

The following five functions can be used to model five light waves. Which of the five waves is not coherent with the other four?

  • A𝑦=0.75ο€»π‘₯2βˆ’πœ‹2sin
  • B𝑦=0.5(π‘₯)sin
  • C𝑦=8(π‘₯)sin
  • D𝑦=2(π‘₯)sin
  • E𝑦=(π‘₯)sin

Q8:

The following five functions can be used to model five light waves.

  1. 𝑦=(π‘₯)sin
  2. 𝑦=2(π‘₯)sin
  3. 𝑦=(2π‘₯)sin
  4. 𝑦=3(π‘₯)sin
  5. 𝑦=0.75(π‘₯)sin

Which of the five waves is not coherent with the other four?

  • Aiv
  • Bi
  • Cii
  • Dv
  • Eiii

Q9:

The following five functions can be used to model five light waves:

  1. 𝑦=3(π‘₯+2πœ‹)sin
  2. 𝑦=2(π‘₯βˆ’2πœ‹)sin
  3. 𝑦=(π‘₯+4πœ‹)sin
  4. 𝑦=0.4ο€»π‘₯+πœ‹2sin
  5. 𝑦=1.8ο€Όπ‘₯βˆ’8πœ‹2sin

Which of the five waves is not coherent with the other four?

  • Aiii
  • Biv
  • Ci
  • Dii
  • Ev

Q10:

The following two functions can be used to model two light waves:

  1. 𝑦=2ο€»3π‘₯+πœ‹2sin
  2. 𝑦=5ο€»π‘˜π‘₯+πœ‹2sin

What value for π‘˜ would make these two waves coherent?

Q11:

The following two functions can be used to model two light waves:

  1. 𝑦=0.5ο€Ό2π‘₯+3πœ‹2sin
  2. 𝑦=0.8(2π‘₯+𝑝)sin

What value for 𝑝 would make these two waves coherent?

  • Aπœ‹
  • B2πœ‹
  • C5πœ‹2
  • D3πœ‹2
  • Eπœ‹2

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