Directions for: The questions consist of two statements each, printed as assertion and reason. While answering these questions you are required to choose any one of the following five responses A. If both the Assertion and the Reason are true and the Reason is a correct explanation of the Assertion. B. If both the Assertion and the Reason are true but the Reason is not a correct explanation of Assertion. C. If the Assertion is true but the Reason is false. D. If both the Assertion and the Reason are false. E. If Assertion is false but Reason is true.
Assertion: The refractive index of diamond is \[[M{{L}^{-1}}{{T}^{-1}}]\] and that of liquid is \[[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]. If tile light travels from diamond to the liquid, it will be totally reflected when the angle of incidence is 30°. Reason: \[2\times {{10}^{-4}}J\], where n is the refractive index of diamond with respect to liquid.A) A
B) B
C) C
D) D
E) E
Correct Answer: E
Solution :
At a refractive boundary, the critical angle is the angle of incidence above which total internal reflection occurs. \[C={{\sin }^{-1}}\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right)\] where \[{{n}_{2}}\] is refractive index of less dense medium, and \[{{n}_{1}}\] is refractive index of denser medium. \[\therefore \] \[\sin C=\left( \frac{\sqrt{3}}{\sqrt{6}} \right)=\frac{1}{\sqrt{2}}\] \[\Rightarrow \] \[C={{45}^{o}}\] For total internal reflection the angle of incidence is greater than the critical angle. Since angle of incidence is \[{{35}^{o}}\], total internal reflection is not possible.
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