Question

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

• A. $0.7\text{cm}$
• B. $1.4\text{cm}$
• C. $2.8\text{cm}$
• D. $10\text{cm}$

Answer 1

The correct option is C $2.8\text{cm}$

Given,

Distance between sun and earth $={10}^{11}\text{m}$

$\therefore$ object distance, $u=-{10}^{11}\text{m}$.

Diameter of the sun $\left(D_s\right)=1.4\times {10}^9\text{m}$

Focal length of concave mirror $\left(f\right)=-2\text{m}$

From the given data, it is clear that the $u>>f$. So it should be considered that the object is placed at infinity. For a concave mirror, when an object is placed at infinity, the image will be formed at focus. i.e. Image distance $v=f=-2\text{m}$

we know that,

$\frac{h_0}{|u|}=\frac{h_i}{|v|}$

Substituting the values in the formula,

$\frac{-v}{u}=\frac{h_i}{h_0}$

$-\frac{(-2)}{-{10}^{11}}=\frac{h_i}{1.4\times {10}^9}$

$\Rightarrow h_i=-\frac{2\times 1.4\times {10}^9}{{10}^{11}}=-2.8\times {10}^{-2}\text{m}\text{or}-2.8\text{cm}$

Hence, the diameter of the image will be $|h_i|=2.8\text{cm}$.

Thus, option (c) is the correct answer.