Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A lens of glass is coated with a thin layer of a clear material of refractive index , which is less than that of the glass. The coating is meant to cut the reflection of light of wavelength nm in air that comes straight on. Find the wavelength of this light inside the coating, the least thickness of the coating and the next greater thickness that also works.
A film in air, light straight on: bright in reflection when , dark when . A coating between air and glass that is less dense than the glass is non-reflecting when . A sheet of index and thickness over one slit moves the pattern by towards that slit.
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 wavelength in the coating. .
Step 2. The least thickness. The two reflected waves cancel when . We want , so . This is a quarter of the wavelength in the coating.
Step 3. The next thickness. With , .
Answer: nm; nm; nm.
Check. The thicker coating is three times the first, as three quarter-wavelengths fit in it.
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