## University Physics with Modern Physics (14th Edition)

Published by Pearson

# Chapter 33 - The Nature and Propagation of Light - Problems - Exercises - Page 1106: 33.35

#### Answer

a. $I_R=0.364I$ b. $I_V=2.70I$.

#### Work Step by Step

The intensity of the scattered light is inversely proportional to the fourth power of the wavelength. Since intensity I is proportional to $\frac{1}{\lambda^4}$, we may write $I=\frac{constant}{\lambda^4}$. a. Take the ratio of the intensity of scattered red light to that of green light. $$\frac{I_R}{I_G}=\frac{\lambda_G^4}{\lambda_R^4}$$ $$\frac{I_R}{I_G}=\frac{(532nm)^4}{(685nm)^4}=0.364$$ $$I_R=0.364I_G$$ b. The shorter the wavelength of light, the more it is scattered. Take the ratio of the intensity of scattered violet light to that of green light. $$\frac{I_V}{I_G}=\frac{\lambda_G^4}{\lambda_V^4}$$ $$\frac{I_V}{I_G}=\frac{(532nm)^4}{(415nm)^4}=2.70$$ $$I_V=2.70I_G$$

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