question_answer

For the same angle of incidence, the angles of refraction in three different media A, B and C are \[\mathbf{15}{}^\circ ,\text{ }\mathbf{25}{}^\circ \] and \[\mathbf{35}{}^\circ \] respectively. In which medium will the velocity of light be minimum?                                                  

Answer:

                As \[\mu =\frac{\sin i}{\sin r}=\frac{c}{\upsilon }\] or \[\upsilon =\frac{\sin r}{\sin i}.c\]                 For a given angle of incidence, \[\upsilon \propto \sin r\]                 \[{{\upsilon }_{A}}\propto \sin {{15}^{\circ }},\]\[{{\upsilon }_{B}}\propto \sin {{25}^{\circ }},\]   \[{{\upsilon }_{C}}\propto \sin {{35}^{\circ }}\]                 But \[\sin {{15}^{\circ }}<\sin {{25}^{\circ }}<\sin {{35}^{\circ }}\]                 \[\therefore \]  \[{{\upsilon }_{A}}<{{\upsilon }_{B}}<{{\upsilon }_{C}}\]                 i.e., velocity of light is minimum in medium A.