A) \[\upsilon O\le {{v}_{E}},{{\mu }_{O}}\le {{\mu }_{E}},\]if the crystal is quartz
B) \[{{\upsilon }_{O}}\ge {{\upsilon }_{E}},{{\mu }_{O}}\le {{\mu }_{E}},\]if the crystal is calcite
C) \[{{\upsilon }_{0}}\ge {{v}_{E}},{{\mu }_{0}}\ge {{\mu }_{E}},\]if the crystal is quartz
D) \[{{\upsilon }_{0}}\le {{v}_{E}},{{\mu }_{0}}\ge {{\mu }_{E}},\]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 - ve and + ve. -ve crystal is calcite for this \[{{\mu }_{E}}<{{\mu }_{O}}\] \[\therefore \] \[{{\upsilon }_{e}}>{{\upsilon }_{O}}\] \[(a=\upsilon e)\] crystal : for quartz crystal \[{{\mu }_{E}}>{{\mu }_{O}}\] \[\therefore \] \[{{\upsilon }_{O}}>{{\upsilon }_{E}}\]
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