# A microscope is focused on a small scratch on the top surface of a glass slide. When a cover slip with athickness of 500 µm is placed on the slide, the microscope must be raised by 120 µm to bring the scratch backinto focus. What is the index of refraction of the cover slip? Assume that all rays entering the microscope makesmall angles with the normal to the slide so that small angle approximation is in effect.

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A microscope is focused on a small scratch on the top surface of a glass slide. When a cover slip with a
thickness of 500 µm is placed on the slide, the microscope must be raised by 120 µm to bring the scratch back
into focus. What is the index of refraction of the cover slip? Assume that all rays entering the microscope make
small angles with the normal to the slide so that small angle approximation is in effect.

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Step 1

Consider the index of refraction of the cover slip be ns, the index of refraction of the air be na, and the thickness of the cover slip be d.

When the cover slip is placed focus of the microscope shifts from point O to O’.

Consider the ray-diagram for the given incidence.

Step 2

From the ray-diagram, use the right-angled triangle property.

Step 3

Write the expression for the Snell’s law.

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