#### 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.
$$\frac{I_V}{I_G}=\frac{\lambda_G^4}{\lambda_V^4}$$
$$\frac{I_V}{I_G}=\frac{(532nm)^4}{(415nm)^4}=2.70$$
$$I_V=2.70I_G$$