Optics finding index of refraction

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The discussion focuses on determining the refractive index of a transparent glass plate by analyzing the behavior of light as it passes through the material. A microscope is used to observe a scratch on the glass, with a noted change in focus after lowering the barrel by 1.87mm, indicating a second image due to refraction. Participants express confusion about how to apply the provided data and the relevance of the equation nglass/nair = y/y'. The challenge lies in correctly interpreting the measurements and calculations to arrive at the refractive index. Clarification on the relationship between the measurements and the refractive index is sought.
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Homework Statement



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In order to determine the refractive index of a transparent plate of glass, a microscope is first focussed on a tiny scratch on the upper surface and the barrel position is recorded. Upon further lowering the microscope barrel by 1.87mm , a focussed image of the scratch is seen again. The plate thickness is 1.5mm. What is the reason for the second image and what is the refractive index of the glass?

Homework Equations



nglass/nair = y/y'

The Attempt at a Solution



i know the reason for the second image, my problem is I'm not sure what to do with the data given, because all that I've tried my answers are too high or to low. I'm also not sure if that equation is relevant, or what to use. I've read my text a few times, and i see nothing that even relates to this problem.
 
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does anyone have an idea?
 

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