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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 obtain the data, a spectrometer was set up with a laser as the light source directed at a diffraction grating labeled with 300 lines per millimetre. The setup was oriented such that the narrow beam of light passed through the grating normally. A diagram should illustrate the following steps:
- Setup: Draw the spectrometer and indicate the light source, grating, and screen.
- Focus: Align the first-order image on the screen using the rotational knob of the spectrometer.
- Measure: Adjust to measure the angle to the second-order images on both sides (left and right) of the central maximum. The angle measured was 40.6° between the left and right images.
- Calculate: Subtract the angles from the central maximum using trigonometric functions to obtain specific angle readings.
Step 2
Step 3
Use the data to calculate the wavelength of the monochromatic light.
Answer
The formula used to calculate the wavelength ( ( \lambda )) is:
Where:
- ( n = 2 ) (for second order)
- ( d = \frac{1}{300 \times 10^{-3}} , \text{m} = 3.33 \times 10^{-6} , \text{m} ) (the grating spacing)
- ( \theta = \frac{40.6°}{2} = 20.3° )
Substituting the values, we have:
Calculating ( \lambda ), we find:
( \lambda = 5.78 \times 10^{-7} , \text{m} ) or (580 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 millimetre results in:
- Greater Angular Separation: Increased separation between images helps in reducing overlap and enhances resolution.
- Smaller Errors: The measurements of the angles yield smaller errors due to more distinct maxima, leading to more precise calculations of wavelength.
Step 5
Give another way of improving the accuracy of this experiment.
Answer
Another way to improve accuracy is to:
- Repeat the Experiment: Take multiple readings for higher or different orders of diffraction and average the results. This helps to reduce random errors.
- Adjust the Spectrometer: Specific adjustments like increasing the diameter of the detector or improving alignment can also enhance measurement accuracy.