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Monochromatic light is incident normally on a diffraction grating that has 4.50 x 10^6 lines m^-1 - AQA - A-Level Physics - Question 19 - 2020 - Paper 1

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Monochromatic light is incident normally on a diffraction grating that has 4.50 x 10^6 lines m^-1. The angle between the second-order diffraction maxima is 44°. What... show full transcript

Worked Solution & Example Answer:Monochromatic light is incident normally on a diffraction grating that has 4.50 x 10^6 lines m^-1 - AQA - A-Level Physics - Question 19 - 2020 - Paper 1

Step 1

Identify the known parameters

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Answer

Given data includes the number of lines on the diffraction grating, which is 4.50 x 10^6 lines/m, and the angle between the second-order diffraction maxima, which is 44°.

Step 2

Calculate the distance between the grating lines

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Answer

The distance 'd' between adjacent grating lines can be calculated using: d=1Nd = \frac{1}{N} where 'N' is the number of lines per meter. Thus, for our grating: d=14.50×1062.22×107md = \frac{1}{4.50 \times 10^6} \approx 2.22 \times 10^{-7} m

Step 3

Apply the diffraction equation for second-order maxima

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Answer

The path difference for diffraction is given by: dsin(θ)=mλdsin(\theta) = m\lambda where:

  • 'm' is the order of the maxima (m = 2 for second order),
  • 'd' is the distance between the grating lines,
  • 'θ' is the angle of diffraction,
  • 'λ' is the wavelength of the light. Substituting the values: 2.22×107sin(44°)=2λ2.22 \times 10^{-7} \cdot sin(44°) = 2\lambda.

Step 4

Calculate the wavelength of the light

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Answer

From the above equation, we can express the wavelength: λ=2.22×107sin(44°)2\lambda = \frac{2.22 \times 10^{-7} \cdot sin(44°)}{2} Calculating this gives: λ2.22×1070.694727.72×107m\lambda \approx \frac{2.22 \times 10^{-7} \cdot 0.6947}{2} \approx 7.72 \times 10^{-7} m Converting meters to nanometers: λ772nm\lambda \approx 772 nm.

Step 5

Identify the correct answer from given options

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Answer

Based on the calculation, the wavelength of the light is approximately 772 nm. Therefore, the correct answer is: C 772 nm.

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