A microscope is focused on a scratch on the bottom of a beaker. Turpentine is poured into the beaker to a depth of 4 cm, and it is found necessary to raise the microscope through a vertical distance of 1.25 cm to bring the scratch again into focus. Find the refractive index of turpentine.

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Solution:

Solution,
Real depth (d) = 4cm
Since the microscope is raised to the vertical distance of 1.25 cm to see the scratch of the bottom of the beaker .
Apparent depth= 4-1.25 =2.75cm
Refractive index of the medium =$\frac{{{\mathop{\rm Re}\nolimits} al{\rm{ Depth}}}}{{Apparent{\rm{ Depth}}}} = \frac{4}{{2.75}} = 1.45$