Physics - Geometrical Optics Question with Solution | TestHub

Convex mirror: $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ with u = -20 cm, f = +20 cm ⇒ v = +10 cm.

$\frac{dv}{dt}=-\frac{v^2}{u^2}\frac{du}{dt}=-\frac{100}{400}(0.5)=-\frac{1}{8}cm/s$

Image height: $h_i=-h_0\frac{v}{u}=-(2)\frac{10}{-20}=+1\mathrm{cm};\frac{d{h}_i}{dt}=-\frac{h_0}{u}\frac{dv}{dt}+\frac{h_{0}v}{u^2}\frac{du}{dt}=\frac{1}{80}cm/s$

$\vec{r}=10\hat{i}+\hat{j},\vec{v}=-\frac{1}{8}\hat{i}+\frac{1}{80}\hat{j}\Rightarrow \vec{r}\cdot \vec{v}=-\frac{10}{8}+\frac{1}{80}=-\frac{99}{80}$ Hence (B).