question_answer

A parallel beam of white light falls on a convex lens, images of blue, yellow and red light are formed on other side of the lens at distances 20 cm, 20.5 cm and 21.4 cm respectively. The disperssive power of the material of the lens is:

A) \[\frac{5}{214}\]                              

B) \[\frac{14}{205}\]

C) \[\frac{619}{1000}\]                       

D) \[\frac{5}{214}\]

Correct Answer: B

Solution :

The refractive index of the material of the lens and hence, the focal length of the lens is different for different colours known as chromatic aberration. The expression for chromatic aberration is \[{{f}_{R}}-{{f}_{B}}=\omega {{f}_{y}}\] where, \[{{f}_{R}},\,{{f}_{B}}\] and \[{{f}_{\gamma }}\]are focal lengths of red, blue and yellow light and \[\omega \]is dispersive power. Putting the numerical values, we have \[\omega =\frac{{{f}_{R}}-{{f}_{B}}}{{{f}_{\gamma }}}=\frac{21.4-20}{20.5}\] \[\omega =\frac{14}{205}\]