A man 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 xx 10^(9) m` and the diameter of the sun's image on the paper is

Options

A. `3.1 xx 10^(-4) cm`
B. `6.5 xx 10^(-5) cm`
C. `6.5 xx 10^(-4) m`
D. `9.2 xx 10^(-4) m`

Answer

D

Explanation

Magnification for convex lens, `m = (-f)/(f-u)`
Here, `f = 10 cm = 10 xx 10^(-2) m, u = 1.5 xx 10^(11) m`
`:. m = (-10 xx 10^(-2))/(10 xx 10^(-2) - 1.5 xx 10^(11)) = 6.67 xx 10^(-13)`
`:.` Diameter of the image,
`d = m xx 1.39 xx 10^(9)`
` = 6.67 xx 10^(-13) xx 1.39 xx 10^(9) = 9.27 xx 10^(-4) m`