Optical Instruments: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Optical Instruments. Understanding the underlying formula is key to arriving at the correct answer below:

The angle subtended by the Sun at the lens is $\alpha = \frac{D}{d} = \frac{1.39 \times 10^9}{1.5 \times 10^{11}} = 0.926 \times 10^{-2} rad$. The image is formed at the focus, so the angle subtended by the image is $\alpha = \frac{d'}{f}$. Thus, the image diameter $d' = \alpha f = 0.926 \times 10^{-2} \times 0.1 = 9.26 \times 10^{-4} m$.