If $\mathrm{l}$ is the intensity of the incident unpolarized light, the intensity transmitted by the first is $\frac{\mathrm{l}}{2}.$ This is the intensity of incident light on the second polaroid. Intensity transmitted by the second polaroid is $\left(\frac{\mathrm{l}}{2}\right){\cos }^2\mathrm{\theta },$ where $\mathrm{\theta }$ is the angle between the axes. Here $\sin \mathrm{\theta }=\frac{3}{5}$, $\cos \mathrm{\theta }$ is therefore $\frac{4}{5}.$

$\frac{\mathrm{l}}{2}{\cos }^2\mathrm{\theta }=\frac{\mathrm{l}}{2}\times {\left(\frac{4}{5}\right)}^2=\frac{8}{25}\mathrm{l}$

$\frac{8}{25}$ is the required ratio