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In an experiment to measure the wavelength of monochromatic light, the angles θ between a central bright image (n = 0) and the first and second order images to the left and right were measured - Leaving Cert Physics - Question 3 - 2016
Question 3
In an experiment to measure the wavelength of monochromatic light, the angles θ between a central bright image (n = 0) and the first and second order images to the l... show full transcript
Worked Solution & Example Answer:In an experiment to measure the wavelength of monochromatic light, the angles θ between a central bright image (n = 0) and the first and second order images to the left and right were measured - Leaving Cert Physics - Question 3 - 2016
Step 1
Describe, with the aid of a labelled diagram, how the data were obtained.
Answer
In the experiment, a laser (vapour lamp) is used as a light source. A diffraction grating and a spectrometer are positioned to measure the angles of the resulting diffraction patterns.
- Set Up the Equipment: Position the laser to direct monochromatic light onto the diffraction grating.
- Measure Distances: Measure the distance (D) from the grating to the screen. This distance is crucial for calculating angles.
- Record Angles: The angles (θ) for the first and second order images (left and right) are recorded using the spectrometer.
- Calculation of Tan: Finally, determine the tangent of the angles from the measurements: where (y) is the position of the image on the screen.
- Labelled Diagram: Include all elements (laser, diffraction grating, and angles) in the diagram for clarity.
Step 2
(i) the wavelength of the light
Answer
To calculate the wavelength of light, we can use the formula: where (d = \frac{1}{500 ext{ lines/mm}} = 2 \times 10^{-6} ext{ m}$$. Using the recorded angles:
- Convert angles to radians: (θ = 36.2° = 0.632 \text{ radians}, θ = 17.2° = 0.300 \text{ radians}, θ = 17.1° = 0.298 \text{ radians}, θ = 36.1° = 0.630 \text{ radians}$$.
- Substitute into the formula for each angle to find the wavelength, averaging the results as necessary.
Step 3
(ii) the maximum number of images that could be observed.
Answer
The maximum number of images can be determined using the formula: . Since (θ_{max} = 90°) implies maximum dispersion through the grating, we find:
- Set (n_{max} = 3) based on the conditions, leading to a total of (1 + 3 + 1 = 5) images observable.
Step 4
Step 5
(ii) the diffraction grating was replaced with a diffraction grating of 300 lines per mm.
Answer
If a grating of 300 lines per mm is used, this will alter the spacing of the lines (d increases). Consequently, the angles for the diffracted images will increase, causing the images to be spaced further apart compared to the original grating. Thus, it would be more difficult to observe closely spaced diffraction patterns.