question_answer

A travelling microscope can move vertically along a scale. It is focused at a mark O on the table and the reading on the vertical scale is\[{{r}_{1}}\]. Now a glass slab is placed over mark O and the microscope has to be moved up to bring the mark in focus again. This time the scale reads\[{{r}_{2}}\]. Lycopodium powder is spread over the top of the glass slab and the microscope is moved up once again to bring the powder particles in sharp focus. This time the vertical scale reads\[{{r}_{3}}\]. Find the refractive index of the material of the glass slab.

A) \[\frac{{{r}_{3}}+{{r}_{1}}}{{{r}_{3}}-{{r}_{2}}}\]  

B) \[\frac{{{r}_{3}}-{{r}_{1}}}{{{r}_{3}}-{{r}_{2}}}\]

C) \[\frac{{{r}_{3}}+{{r}_{2}}}{{{r}_{3}}-{{r}_{1}}}\]  

D) \[\frac{{{r}_{3}}+{{r}_{2}}}{{{r}_{3}}+{{r}_{1}}}\]