How Much Should the Microscope Be Raised After Adding a Plastic Layer?

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To refocus a microscope after placing a 1cm thick plastic layer with an index of refraction of 1.67 over a black dot, the objective must be raised due to the apparent depth change caused by refraction. The black dot will appear closer, similar to how a swimming pool looks shallower than it is. A specific equation relates the refractive index to real and apparent depth, which is essential for solving the problem. Understanding this relationship is crucial for determining the necessary adjustment in the microscope's height. Proper guidance on the relevant formulas and concepts can help clarify the solution process.
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Problem:
A microscope is focussed on a black dot. You place a 1cm thick piece of plastic, with an index of refraction of 1.67, over the dot. By how much must you raise the microscope's objective for the dot to be in focus again?

Ok, so I'm not sure how to that question at all. Waves and Lights don't seem to click well with me, and it's hard to visualize the problem. I don't even know what formula(s) I would use.

Any help with these is really appreciated! I just need to be steered in the right direction
Thank you very much!
 
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I solved the first problem posted, so I deleted it.
I still need major help with this one though!
 
The black dot will appear to be closer,for the same reason that a swimming pool seems to be shallower.There is a simple equation linking refractive index with real depth and apparent depth.
 
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