A) \[{{\upsilon }_{O}}\le {{\mu }_{O}}\le {{\mu }_{E}},\]if the crystal is quartz
B) \[{{\upsilon }_{O}}\ge {{\upsilon }_{E}},{{\mu }_{O}}\le {{\mu }_{E}},\]if the crystal is calcite
C) \[{{\upsilon }_{o}}\ge {{\upsilon }_{E}},{{\mu }_{o}}\ge {{\mu }_{E}},\]if the crystal is quartz
D) \[{{\upsilon }_{1}}\le {{\upsilon }_{E}},{{\mu }_{o}}\ge {{\mu }_{E}},\]if the crystal is calcite.
Correct Answer: D
Solution :
In double refraction light rays always split into two, ordinary and extraordinary. O-waves has same velocity in all direction but E-waves has different velocity in different directions. Along optic axis O and E waves have same velocity uniaxial crystal are of two types \[-\,\text{ve}\]and \[+\,\text{ve}\text{.}\] \[-\,\text{ve}\]crystal is calcite for this \[{{\mu }_{E}}<{{\mu }_{O}}\] \[\therefore \] \[{{\upsilon }_{e}}>{{\upsilon }_{O}}\] \[(+\,\upsilon e)\]crystal: for quartz crystal \[{{\mu }_{E}}>{{\mu }_{O}}\] \[\therefore \] \[{{\upsilon }_{O}}>{{\upsilon }_{E}}\]
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