Question

A square glass slab of thickness 15 cm contains a small air bubble. Its apparent depth on looking through one face is 7 cm and when viewed through the opposite face is 3 cm. Calculate the refractive index of the glass slab.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Let}{\mathrm{x}}_1\mathrm{be}\mathrm{the}\mathrm{real}\mathrm{distance}\mathrm{of}\mathrm{the}\mathrm{bubble}\mathrm{from}\mathrm{one}\mathrm{side}\mathrm{and}{\mathrm{x}}_2\mathrm{be}\mathrm{the}\mathrm{real}\mathrm{distance}\mathrm{from}\mathrm{other}\mathrm{side}, \\ \mathrm{\mu }=\frac{\mathrm{real}\mathrm{distance}}{\mathrm{apparent}\mathrm{distance}} \\ \mathrm{\mu }=\frac{{\mathrm{x}}_1}{7} \\ {\mathrm{x}}_1=7\mathrm{\mu } \\ \mathrm{When}\mathrm{viewed}\mathrm{from}\mathrm{other}\mathrm{side}, \\ \mathrm{\mu }=\frac{{\mathrm{x}}_2}{3} \\ {\mathrm{x}}_2=3\mathrm{\mu } \\ \mathrm{Total}\mathrm{thickness}\mathrm{of}\mathrm{slab}={\mathrm{x}}_1+{\mathrm{x}}_2 \\ 15=7\mathrm{\mu }+3\mathrm{\mu } \\ 15=10\mathrm{\mu } \\ \mathrm{\mu }=\frac{15}{10}=1.5 \end{gathered}$$