A physics club is testing a diffraction grating that is marked with 450 lines in each millimetre…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A physics club is testing a diffraction grating that is marked with lines in each millimetre. The members shine two lasers on it together, both at right angles to the grating. One laser gives light of wavelength nm. The wavelength of the other laser is not marked. The grating is held in a frame so that the lasers shine straight on to it, and the wall is far away. The club wants to know what can be seen on the wall, and how many bright spots each laser makes. On the wall the club sees a match. The fourth bright spot of the second laser falls at exactly the same angle as the third bright spot of the nm laser, on the same side. Find the second wavelength and the angle at which the two spots meet. Find also the highest order of each laser light that can be seen on the wall.
Need a reminder? The key ideaShow
A grating of spacing gives bright lines at . The highest order has . In a real double slit, an order is missing when , and the orders inside the central maximum have .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The second wavelength. At the same angle, . We want , so .
Step 2. The spacing. .
Step 3. The angle. , so .
Step 4. The highest orders. For nm: , so the highest order is . For nm: , so the highest order is .
Answer: nm; ; orders and .
Check. The meeting is at the third order of the longer wavelength, which is its highest order. At that angle the shorter wavelength is only at its fourth order, and it has one more order after it.
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