A) 3/4
B) 3/5
C) 5/3
D) 5/4
Correct Answer: C
Solution :
Let \[{{\lambda }_{g}}\] and \[{{\lambda }_{w}}\] be the wavelengths in glass and water respectively. Number of waves in glass slab of thickness \[8\,cm=\frac{8}{\lambda g}\]S Number of waves in water. According to the question, (10 cm) \[=\frac{10}{\lambda w}\] \[\frac{8}{{{\lambda }_{g}}}=\frac{10}{{{\lambda }_{w}}}\] \[\Rightarrow \] \[\frac{{{\lambda }_{w}}}{{{\lambda }_{g}}}=\frac{5}{4}\] We have \[{{\mu }_{g}}=\frac{C}{{{v}_{g}}}\] and \[{{\mu }_{w}}=\frac{C}{{{V}_{w}}}\] \[\frac{{{\mu }_{g}}}{{{\mu }_{w}}}=\frac{{{v}_{w}}}{{{v}_{g}}}=\frac{n\,{{\lambda }_{w}}}{n\,{{\lambda }_{g}}}=\frac{{{\lambda }_{w}}}{{{\lambda }_{g}}}\] \[{{\mu }_{g}}=\frac{{{\lambda }_{w}}}{{{\lambda }_{g}}}\times {{\mu }_{w}}=\frac{5}{4}\times \frac{4}{3}=\frac{5}{3}\]
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