Question

The diameter of the sun is 1.4 × 10⁹ m and its distance from the earth is 1.5 × 10¹¹ m. Find the radius of the image of the sun formed by a lens of focal length 20 cm.

Answer 1

Given,
Diameter of the sun = 1.4 × 10⁹ m
Distance between sun and earth is taken as object distance (u) = − 150 × 10¹¹ cm,
Focal length (f) of the lens = 20 cm
Using lens formula,
\[\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\]
The object distance is very large as compared to focal length of the lens.
Hence, the image is formed at the focus.
\[\Rightarrow   \frac{1}{v} = \frac{1}{20} - \frac{1}{150 \times {10}^{11}}\] 
\[= \frac{750 \times {10}^9 - 1}{150 \times {10}^{11}}\]
\[\simeq \frac{750 \times {10}^9}{150 \times {10}^{11}}\]

\[\Rightarrow   v = \frac{150 \times {10}^{11}}{750 \times {10}^9}\] 
We know, Magnification (m) is given by:
\[(m) = \frac{v}{u} = \frac{h_2}{h_1}\]
\[\Rightarrow    h_2  = \frac{v}{u} \times  h_1\] 

\[= \frac{150 \times {10}^{11}}{750 \times {10}^9 \times 150 \times {10}^{11}} \times 0 . 7 \times  {10}^{12}   mm\] 

\[ = 0 . 93  mm\]
Hence, the required radius of the image of the sun is 0.93 mm.