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In an experiment to measure the wavelength of monochromatic light, a narrow beam of the light fell normally on a diffraction grating - Leaving Cert Physics - Question 2 - 2006
Question 2
In an experiment to measure the wavelength of monochromatic light, a narrow beam of the light fell normally on a diffraction grating. The grating had 300 lines per m... show full transcript
Worked Solution & Example Answer:In an experiment to measure the wavelength of monochromatic light, a narrow beam of the light fell normally on a diffraction grating - Leaving Cert Physics - Question 2 - 2006
Step 1
Describe, with the aid of a labelled diagram, how the data was obtained.
Answer
To describe how the data was obtained, one would typically include a diagram showing the following components:
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Apparatus Setup: A spectrometer, grating labelled with the number of lines per mm, a laser, and a screen to observe the diffraction pattern.
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Process: Align the laser so that it strikes the grating normally. Focus or line up the laser to measure angles accurately by documenting the measurements on the screen.
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Angle Measurements: Record the angle between the 2nd order images on the left and right of the central bright image. For each measurement, subtract the readings to achieve the final angle, using trigonometric functions to measure the angle accurately, such as using θ as the angle for calculations.
Step 2
Step 3
Use the data to calculate the wavelength of the monochromatic light.
Answer
To calculate the wavelength (λ) of the monochromatic light, we can use the diffraction formula:
where:
- = order of the image (2 for second order)
- = distance between lines on the grating, calculated as
- = angle measured, in this case, 20.3° for either side of the central maximum, hence:
Using the value of n: [ λ = \frac{d}{\text{sin}(\theta)} ] [ λ = \frac{3.33 \times 10^{-6}}{\text{sin}(20.3^{ ext{o}})} = 5.78 \times 10^{-7}\text{ m} = 578\text{ nm}]
Step 4
Explain how using a diffraction grating of 500 lines per mm leads to a more accurate result.
Answer
Using a diffraction grating with 500 lines per mm provides:
- Greater Resolution: More lines increase the ability to resolve closer wavelengths due to the larger number of path differences that facilitate clear maxima and minima.
- Increased Angular Separation: As the number of lines increases, the angular distances between different order images also increase, helping to reduce overlap and allowing more precise angle measurements.
Step 5
Give another way of improving the accuracy of this experiment.
Answer
To improve accuracy, one could repeat the experiment by averaging results obtained from different measurements or different orders. Additionally, increasing the distance to the screen or altering the measurement method for angles using a better protractor can enhance precision.