A) \[{{\mu }_{1}}={{\mu }_{2}}\]
B) \[{{\mu }_{2}}={{\mu }_{3}}\]
C) \[{{\mu }_{3}}={{\mu }_{4}}\]
D) \[{{\mu }_{1}}={{\mu }_{4}}\]
Correct Answer: D
Solution :
According to given figure \[_{1}{{\mu }_{2}}=\frac{\sin i}{\sin {{r}_{1}}}\] ?(1) \[_{2}{{\mu }_{3}}=\frac{\sin {{r}_{1}}}{\sin {{r}_{2}}}\] ?.(2) and \[_{3}{{\mu }_{4}}=\frac{\sin {{r}_{2}}}{\sin {{r}_{3}}}\] ?.(3) On multiplying eqs. (1), (2) and (3), we get \[\frac{\sin i}{\sin {{r}_{1}}}\times \frac{\sin {{r}_{1}}}{\sin {{r}_{2}}}\times \frac{\sin {{r}_{2}}}{\sin {{r}_{3}}}\] \[=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}\times \frac{{{\mu }_{3}}}{{{\mu }_{2}}}\times \frac{{{\mu }_{4}}}{{{\mu }_{3}}}\] Or \[\frac{\sin i}{\sin {{r}_{3}}}=\frac{{{\mu }_{4}}}{{{\mu }_{1}}}\] Or \[{{\mu }_{1}}\sin i={{\mu }_{4}}\sin {{r}_{3}}\] Since, AB is parallel to CD so, \[i={{r}_{3}}\] Therefore, \[{{\mu }_{1}}={{\mu }_{4}}\]
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