Index of when refraction/optics question

[Gino97]

The question
A microscope is focused on a black dot. When a 1.20 cm -thick piece of plastic is placed over the dot, the microscope objective has to be raised 0.380 cm to bring the dot back into focus.

What is the index of refraction of the plastic

Relevant equations/ideas
n1*sin(theta1)=n2*sin(theta2)

Trying to solve
I know I must use triangles to figure out the angles needed for Snells law, but have more unknown variables than equations to relate them so I don't know how to solve for them

 

[Merlin3189]

Have you come across real and apparent depth? For example, when you look into a pool of water, it appears shallower than it really is, due to refraction.

Also, you could pick an arbitrary angle and do the calculation for that. Edit: And I'd always start with a diagram (or several.)