Question

The ratio of the diameter of the sun to the distance between the earth and the sun is approximately $0.009$. The approximate diameter of the image of the sun formed by a concave spherical mirror of radius of curvature $0.4m$ is

• A. $4.5\times 10^{-6}m$
• B. $4.0\times 10^{-6}m$
• C. $3.6\times 10^{-3}m$
• D. $1.8\times 10^{-3}m$

Answer 1

Answer: (D)

The angle subtended by sun on mirror
$Q=\frac{D}{d_{SE}}=\frac{d}{f}$
$\therefore d=\frac{D}{d_{SE}}\times f$
According to the question,
$\frac{D}{d_{SE}}=0\cdot 009$
$f=\frac{r}{2}=\frac{0.4}{2}=0\cdot 2m$
$\therefore d=0\cdot 009\times 0.2m$
$=9\times 2\times 10^{-4}m$
$=18\times 10^{-4}m$
$=1.8\times 10^{-3}m$