Question

A glass slab of thickness 10 cm contains same number of waves as 12 cm of water, when both are transversed by same monochromatic light. If refractive index of water is $\frac{4}{3}$, what is the refractive index of the glass (material of slab)?

• A. 1.5
• B. 1.6
• C. 1.7
• D. 1.8

Answer 1

The correct option is B 1.6

Say 'N' is the number of waves.

Thickness, $t=N\times \frac{\lambda }{{\mu }_{glass}}10=N\times \frac{\lambda }{{\mu }_{glass}}$
Similarly for water,

$12=N\times \frac{\lambda }{{\mu }_{water}}=N\times \frac{\lambda }{\frac{4}{3}}\frac{10}{12}=\frac{\lambda }{{\mu }_{glass}}\times \frac{4}{3\lambda }\Rightarrow {\mu }_{glass}=\frac{4\times 12}{3\times 10}=1.6$