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A diffraction grating has 500 lines per mm - AQA - A-Level Physics - Question 17 - 2018 - Paper 1

Question 17

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A diffraction grating has 500 lines per mm. When monochromatic light is incident normally on the grating the third-order spectral line is formed at an angle of 60° f... show full transcript

Worked Solution & Example Answer:A diffraction grating has 500 lines per mm - AQA - A-Level Physics - Question 17 - 2018 - Paper 1

Step 1

Calculate the Wavelength of the Monochromatic Light

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Answer

To find the wavelength of the monochromatic light, we can use the diffraction grating equation:

$d \sin(\theta) = m \lambda$

Where:

$d$ is the distance between grating lines,
$\theta$ is the diffraction angle,
$m$ is the order of the spectrum (in this case, $m = 3$ ), and
$\lambda$ is the wavelength.

Calculate $d$ : Given that there are 500 lines per mm, the distance between grating lines, $d$ , can be calculated as: $d = \frac{1}{500 \text{ lines/mm}} = 0.002 ext{ mm} = 2 \times 10^{-6} ext{ m}$
Use the Diffraction Equation: Plugging in the known values into the diffraction equation:

$2 \times 10^{-6} \sin(60°) = 3 \lambda$
Calculate $\sin(60°)$ : This gives: $\sin(60°) = \frac{\sqrt{3}}{2}$
Rearranging the Equation for $\lambda$ : Now we can rearrange the equation to find $\lambda$ : $\lambda = \frac{2 \times 10^{-6} \cdot \frac{\sqrt{3}}{2}}{3} = \frac{\sqrt{3} \times 10^{-6}}{3} m$
Convert to nm: Calculating this gives us:

$\lambda \approx 0.577 \times 10^{-6} m = 577 nm$

By selecting the closest option from the given choices, we find the wavelength of the monochromatic light is approximately 580 nm, thus the correct answer is B.

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A diffraction grating has 500 lines per mm - AQA - A-Level Physics - Question 17 - 2018 - Paper 1

Worked Solution & Example Answer:A diffraction grating has 500 lines per mm - AQA - A-Level Physics - Question 17 - 2018 - Paper 1

Calculate the Wavelength of the Monochromatic Light

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