question_answer

Speed of light waves in two mediums A and B are  \[1.8\times {{10}^{8}}m/s\] and \[2.5\times {{10}^{8}}m/s,\] respectively. What is the critical angle for this pair of mediums?

Answer:

\[46{}^\circ 1'\] Given, \[{{V}_{A}}=1.8\times {{10}^{8}}m/s,\]\[{{V}_{B}}=2.5\times {{10}^{8}}m/s\] \[\therefore \]Refractive index of medium A, \[{{n}_{1}}=\frac{{{C}_{0}}}{{{V}_{A}}}=\frac{3\times {{10}^{8}}}{1.8\times {{10}^{8}}}=\frac{5}{3}\] and Refractive index of medium B, \[{{n}_{2}}=\frac{{{C}_{0}}}{{{V}_{B}}}=\frac{3\times {{10}^{8}}}{2.5\times {{10}^{8}}}=\frac{6}{5}\] Since,                \[{{n}_{1}}>{{n}_{2}}\] \[\therefore \] Medium A is denser with respect to medium B. Thus, critical angle in medium A for total internal reflection, \[{{\theta }_{C}}={{\sin }^{-1}}\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right)={{\sin }^{-1}}\left( \frac{6/5}{5/3} \right)={{\sin }^{-1}}\left( \frac{18}{25} \right)=46{}^\circ 1'\]