Question

The sun's diameter is $1.4\times {10}^{9}m$ and its distance from the earth is ${10}^{11}m$. Determine the diameter of its image, formed by a convex lens of focal length $2m$.

• A. $0.7cm$
• B. $1.4cm$
• C. $2.8cm$
• D. $Zero(i.e.pointimage)$

Answer 1

The correct option is B $1.4cm$

In the given problem,

$u=-{10}^{11}$ m

Since, focal length is very small as compared to the object distance, it is considered that the image is formed at focus.

$v=2$ m

Magnification, $m=\frac{v}{u}=\frac{h_{image}}{h_{object}}$

$\therefore h_{image}=v\frac{h_{object}}{u}$

$\therefore h_{image}=2\times \frac{1.4\times {10}^9}{{10}^{11}}$

$\therefore h_{image}=2.8$ cm

$\therefore radius=2.8/2=1.4$ cm