A teacher builds a double-slit experiment for a class…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A teacher builds a double-slit experiment for a class. The wavelength is nm, the slits are mm apart and the screen is m away. She then covers the upper slit with a thin transparent sheet of refractive index , and she sees the whole pattern move. The central bright fringe has moved to the place where the th bright fringe of the old pattern was. The class draws the pattern on the screen with a pencil before and after the sheet is added, so the shift can be read at once with a ruler. The class wants to know how thick the sheet is. Find the fringe width, the thickness of the sheet and the shift of the central fringe. Then the teacher puts a second sheet, of refractive index , over the lower slit, and the central fringe goes back to the middle of the screen. Find the thickness of the second sheet.
Need a reminder? The key ideaShow
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.
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 fringe width. .
Step 2. The first sheet. A shift of fringes needs an extra path of . We want , so .
Step 3. The shift. .
Step 4. The second sheet. The two extra paths must be equal: . So .
Answer: mm; ; mm; .
Check. The second sheet has a smaller index, so it must be thicker to give the same extra path. The ratio of the thicknesses is , which is .
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