PROBLEMS
- Author:
- Timo Budarz
- A single slit of width 1/20 mm has laser light of 633 nm passing through it. What is the width of the central maximum on a screen that is 3.0 m beyond the slits?
- Does a smaller slit width make for a larger or smaller pattern on a screen? Why should this be? Explain in words besides just referring to the equation.
- Does a longer or shorter wavelength make for a smaller pattern on the screen. Why should this be? Explain in words besides just referring to the equation.
- If we consider a real double slit, what ratio of d/a is required to fit 5 peaks within the central single slit maximum?
- What ratio of d/a makes the 3rd order maximum (3rd peak from center) of the double slit pattern match the second minimum of the single slit pattern?
- A person is viewing two cars in traffic on a freeway as they ascend in an airplane. Suppose the cars are 4.0 m apart. At what altitude are the cars unable to be resolved by the person in the plane who has pupils of 3 mm diameter regardless of color? What colored cars would be easier to resolve at a higher altitude?
- The atmosphere limits the ability of a terrestrial telescope to resolve distant stars because it deflects the path of starlight in a random way due to tiny changes in air's refractive index along the light's path to the ground. (This is the major advantage of the Hubble telescope being in space.) The random deflection of the starlight means that even a sharp point of starlight becomes spread over what's called a seeing disk of an angular size that depends on atmospheric conditions. It's like smudging an ink spot with your finger. The angular size of the seeing disc ranges from 0.4 arc seconds to around 3 arc seconds between excellent and rather poor conditions. What diameter of telescope tube is required in each of those cases such that the resolution of the stars is NOT limited by diffraction? Write your answer as , where x is the value you determine for each case. Assume wavelength is 550nm.
- A photo is printed at 100 dpi (dots per linear inch). At distances smaller than what value of d should the photo appear pixelated if your pupil diameter is 3.0 mm?
- Is it possible for the central peak from the single slit pattern to be narrower than the central peak from a multiple slit pattern? Explain.
ANSWERS
1. 7.6cm
2. Smaller slit means bigger pattern. Need bigger angle to provide a sufficient path length difference to induce any significant phase difference leading to the interference pattern.
3. Smaller pattern for shorter wavelength so that small path length differences equate to relatively larger phase differences.
4. 5/2
5. 3/2
6. 24,600m
7. D>34cm; D>4.6 cm
8. 61.5 inches = 156 cm
9. No. a<d is required by geometry, so phase arguments cannot lead to this conclusion.