Question

The suns diameter is $1.4\times {10}^{9}m$ and its distance from the earth is ${10}^{11}m$. The diameter of its image, formed by a convex mirror of focal length 2m will

• A. 0.7 cm
• B. 1.4 cm
• C. 2.8 cm
• D. 10 cm

Answer 1

The correct option is C 2.8 cm

Distance from earth (v) = ${10}^{11}\text{m}$

Diameter of the sun = $1.4\times {10}^9\text{m}$

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

$\text{m =}\frac{\text{v}}{\text{u}}=\frac{{\text{h}}_{\text{i}}}{{\text{h}}_{\text{o}}}$

Substituting the values in the formula,

$\frac{\text{v}}{\text{u}}=\frac{{\text{h}}_{\text{i}}}{{\text{h}}_{\text{o}}}$

$\frac{2}{{10}^{11}}=\frac{{\text{h}}_{\text{i}}}{1.4\times {10}^9}$

${\text{h}}_{\text{i}}\text{=}\frac{2\times 1.4\times {10}^9}{{10}^{11}}$

${\text{h}}_{\text{i}}\text{= 2}\text{.8}\times \text{1}{\text{0}}^{-2}\text{m}$

${\text{h}}_{\text{i}}\text{= 2}\text{.8 cm}$

The diameter of the image will be 2.8 cm