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Question

The suns diameter is 1.4×109m and its distance from the earth is 1011m. The diameter of its image, formed by a convex mirror of focal length 2m will

A
0.7 cm
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B
1.4 cm
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C
2.8 cm
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D
10 cm
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Solution

The correct option is C 2.8 cm
Distance from earth (v) = 1011 m
Diameter of the sun = 1.4×109 m
Focal length of convex mirror (f) = 2 m
From the given data, it is clear that the v>>f. So it should be considered that the object is placed at infinity.
For a convex mirror, when an object is placed at infinity, image will be formed at focus. i.e.
v = f = 2 m
We know the formula
m = vu= hiho
Substituting the values in the formula,
vu= hiho
21011= hi1.4×109
hi = 2×1.4×1091011
hi = 2.8×102 m
hi = 2.8 cm
The diameter of the image will be 2.8 cm


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