Hint: Apply Snell's Law and Refractive index formula to get the answer
Snell's Law describes the relationship between the angles of the two light waves and the indices of refraction of the two materials as:
n1 x sin(q1) = n2 x sin(q2)
Refractive Index (n) = D(measured)/D(apparent)
where D(measured) is the measured depth (from the surface of the liquid to the position of the mark on the empty cell) using the microscope, and D(apparent) is the mark measurement with and without liquid.