Question

The diameter of the sun is $1.4\times {10}^9\text{m}$ and its distance from the earth is $1.5\times {10}^{11}\text{m}$. Find the radius of the image of the sun formed by a lens of focal length 20 cm.

Answer 1

Here, $u=-150\times {10}^{11}\text{cm}$

f = 20 cm

Using lens formula,

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{1}{v}=\frac{1}{20}-\frac{1}{150\times {10}^{11}}$

$=\frac{750\times {10}^9-1}{150\times {10}^{11}}$

$=\frac{750\times {10}^9}{150\times {10}^{11}}$

$\Rightarrow v=\frac{150\times {10}^{11}}{750\times {10}^9}$

We know, Magnification,

$\left(m\right)=\frac{v}{u}=\frac{h_2}{h_1}$

$\Rightarrow h_2=\frac{v}{u}\times h_1$

$=\frac{150\times {10}^{11}}{750\times {10}^9\times 150\times {10}^{11}}\times 0.7\times {10}^{11}\text{mm}$

$=0.93\text{mm}$