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Image Formation by a Convex Lens
Concepts tested here
- Magnification for a very distant object
All Questions
2008 AIPMT 1 question
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A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the Sun is $1.39 \times 10^{9}$ m and its mean distance from the earth is $1.5 \times 10^{11}$ m. What is the diameter of the Sun's image on the paper ?The Sun is very far away, so its rays are practically parallel and the image is formed in the focal plane of the lens.
Object distance $u = 1.5 \times 10^{11}$ m; image distance $v = f = 10$ cm $= 0.1$ m
Magnification: $\dfrac{h_i}{h_o} = \dfrac{v}{u}$
$\Rightarrow \dfrac{h_i}{1.39 \times 10^{9}} = \dfrac{0.1}{1.5 \times 10^{11}}$
$h_i = \dfrac{0.1 \times 1.39 \times 10^{9}}{1.5 \times 10^{11}}$
$h_i = \dfrac{1.39 \times 10^{8}}{1.5 \times 10^{11}}$ m
$h_i = 9.2 \times 10^{-4}$ m
So the diameter of the Sun's image on the paper is about $9.2 \times 10^{-4}$ m.