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A Level · AS · structured

AS Level foundations · Question 9

AS Level foundations · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
demanding
Marks
11
Topics
2
Answer
Complete
Light diffracted by a grating into orders either side of the straight-through directionλ = 590 nmdiffraction grating500 lines per mmn = 0n = 1n = 1n = 2n = 2θnot to scale
Fig. 9.1A parallel beam of light of wavelength 590 nm travels from the left and meets a diffraction grating at normal incidence; the grating is drawn edge-on as a narrow ruled strip and labelled 500 lines per mm. On the far side five beams spread from the grating: one continues straight through and is labelled n = 0, and above and below it lie beams labelled n = 1 and, at larger angles, n = 2. An arc marks the angle θ between the straight-through direction and the upper second-order beam. The angles drawn are not to scale.
structured11 marks

Coherent light of wavelength 590 nm is incident normally on a diffraction grating with 500 lines per millimetre. The diffracted light is observed on a screen a long way from the grating.

  1. (a)

    State State what is meant by coherent.

    2 marks
  2. (b)

    Calculate Calculate the angle between the second-order maximum and the straight-through direction.

    3 marks
  3. (c)

    Determine Determine the highest order of maximum that can be observed with this grating and this light.

    3 marks
  4. (d)

    Explain The grating is replaced by one with 300 lines per millimetre. Explain, without calculation, how this changes the pattern observed.

    3 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: the waves have a constant phase difference which requires them to have the same frequency (and, in practice, the same wavelength) d = 1 / (500 × 10³) = 2.0 × 10⁻⁶ m
01

(a)

2 marks

State State what is meant by coherent.

How to approach it

Answer the command word directly and use precise physical vocabulary. Include only the distinct features or facts that earn marks, without burying them in unrelated background information.

  1. 1

    the waves have a constant phase difference

  2. 2

    which requires them to have the same frequency (and, in practice, the same wavelength)

02

(b)

3 marks

Calculate Calculate the angle between the second-order maximum and the straight-through direction.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    d = 1 / (500 × 10³) = 2.0 × 10⁻⁶ m

  2. 2

    sin θ = nλ/d = 2 × 590 × 10⁻⁹ / 2.0 × 10⁻⁶ = 0.590

  3. 3

    Taking the inverse sine of the second-order ratio gives θ = 36.2°.

03

(c)

3 marks

Determine Determine the highest order of maximum that can be observed with this grating and this light.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    the maximum possible value of sin θ is 1, so n ≤ d/λ

  2. 2

    d/λ = 2.0 × 10⁻⁶ / 590 × 10⁻⁹ = 3.39

  3. 3

    n must be a whole number, so the highest order observed is the third

04

(d)

3 marks

Explain The grating is replaced by one with 300 lines per millimetre. Explain, without calculation, how this changes the pattern observed.

How to approach it

State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.

  1. 1

    the slit separation d is larger

  2. 2

    so for each order sin θ = nλ/d is smaller and every maximum moves closer to the centre

  3. 3

    and because d/λ is larger, more orders can be seen

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