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 $0.4\, m$ is

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

Answer 1

Answer: (D)

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