The focal lengths of a convex lens for red an | vedclass

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(B) The dispersive power $\omega$ of a lens is defined as $\omega = \frac{f_R - f_V}{f_y}$, where $f_R$ is the focal length for red light, $f_V$ is th

Vedclass · Accepted Answer

$0.0325$

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(B) The dispersive power $\omega$ of a lens is defined as $\omega = \frac{f_R - f_V}{f_y}$, where $f_R$ is the focal length for red light, $f_V$ is the focal length for violet (or blue) light, and $f_y$ is the mean focal length.For a thin lens, the mean focal length is approximately $f_y = \sqrt{f_R f_V}$.Given: $f_R = 100 	ext{ cm}$, $f_V = 96.8 	ext{ cm}$.First, calculate the mean focal length: $f_y = \sqrt{100 	imes 96.8} = \sqrt{9680} \approx 98.387 	ext{ cm}$.Now, calculate the dispersive power: $\omega = \frac{100 - 96.8}{98.387} = \frac{3.2}{98.387} \approx 0.0325$.Thus, the correct option is $B$.

The focal lengths of a convex lens for red and blue light are $100 \text{ cm}$ and $96.8 \text{ cm}$ respectively. The dispersive power of the material of the lens is:

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