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Question: A man is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of...

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 1.39×109 m1.39 \times 10 ^ { 9 } \mathrm {~m} and its mean distance from the earth is 1.5×10111.5 \times 10 ^ { 11 } m, the diameter of the sun’s image on the paper is :

A

3.1×10−4 m3.1 \times 10 ^ { - 4 } \mathrm {~m}

B

6.5×10−5 m6.5 \times 10 ^ { - 5 } \mathrm {~m}

C

6.5×10−4 m6.5 \times 10 ^ { - 4 } \mathrm {~m}

D

9.2×10−4 m9.2 \times 10 ^ { - 4 } \mathrm {~m}

Answer

9.2×10−4 m9.2 \times 10 ^ { - 4 } \mathrm {~m}

Explanation

Solution

: Magnification for

Here, f=10 cm=10×10−2 m\mathrm { f } = 10 \mathrm {~cm} = 10 \times 10 ^ { - 2 } \mathrm {~m}

∴m=−10×10−210×10−2−1.5×1011=6.67×10−13\therefore \mathrm { m } = \frac { - 10 \times 10 ^ { - 2 } } { 10 \times 10 ^ { - 2 } - 1.5 \times 10 ^ { 11 } } = 6.67 \times 10 ^ { - 13 }

∴\thereforeDiameter of the image

d=m×1.39×109\mathrm { d } = \mathrm { m } \times 1.39 \times 10 ^ { 9 }

=6.67×10−13×1.39×109=9.27×10−4 m= 6.67 \times 10 ^ { - 13 } \times 1.39 \times 10 ^ { 9 } = 9.27 \times 10 ^ { - 4 } \mathrm {~m}