question_answer

If red light and violet light have the focal lengths \[{{f}_{r}}\] and\[{{f}_{v}}\]respectively, then which one of the following is correct?

A)  \[{{\lambda }_{r}}\le {{\lambda }_{v}}\]      

B)  \[{{\mu }_{r}}>{{\mu }_{v}}\]

C)  \[{{\mu }_{r}}<{{\mu }_{v}}\]         

D)  \[{{\lambda }_{r}}>{{\lambda }_{v}}\]

Correct Answer: C

Solution :

Key Idea: Red light bends the least in dispersion of white light by prism. The focal length of a lens, with refractive index \[(\mu )\] is given by \[\frac{1}{f}=(\mu -1)\,\left( \frac{1}{{{R}_{1}}-{{R}_{2}}} \right)\] where \[{{R}_{1}}\] and \[{{R}_{2}}\] are radii of curvatures of the first and second surfaces, respectively. \[\Rightarrow \] \[f\propto \frac{1}{\mu }\]. Since, \[{{f}_{v}}<{{f}_{r}}\] Alternative: We know that in a material medium the light rays of different colours travel with different speeds. In glass, the speed of violet light is minimum while that of red light is maximum. Therefore, the refractive index of glass is maximum for violet light, and minimum for red light i. e., \[{{\mu }_{r}}<{{\mu }_{v}}\].