A glass-maker is checking a thin plate that will be used as a camera filter…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A glass-maker is checking a thin plate that will be used as a camera filter. The plate is flat, with two parallel faces. A green lamp shines on it straight on. The light of the lamp has a wavelength of nm in air. The plate is mm thick and its refractive index is . The maker wants a picture of how many waves are packed into the plate. The maker also wants to know how much the plate delays the light, compared with a gap of air of the same thickness. The lamp is steady and the plate is clean, so no light is lost in the glass, and the plate has no coating. Use m/s. Find the wavelength in the glass and the number of wavelengths that fit across the plate. Find the number of wavelengths that fit across the same thickness of air. Then find how much longer the light takes to cross the plate than to cross that air.
Need a reminder? The key ideaShow
A wavefront is a surface of equal phase, and a ray is at right angles to it. In a medium of index the speed is and the wavelength is , while the frequency stays the same. Snell's law follows from Huygens' construction.
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.
Given. nm, mm and .
Step 1. The wavelength in the glass. .
Step 2. Waves across the glass. .
Step 3. Waves across the same air. . The plate holds times as many waves, because the wavelength is shorter.
Step 4. The extra time. In the glass the time is , and in air it is . The difference is .
Answer: nm; waves; waves; ps.
Check. The extra number of waves is . This is . Hold on to this number: it decides how a thin sheet moves the fringes in course three.
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