Question

at what distance from the sun is the intensity of sunlight two times the value at the earth. ( the average earth-sun separation is 1.496x 10^11 m

a. 7.4 x 10^10 m

b. 1.06 x 10 ^ 11 m

c. 2.99 x10^ 11 m

Answer 1

For point or spherical sources, the intensity varies with distance as ------(i) [where r = distance]

1 Ια -2

given:

r1 = distance between sun and earth = $1.496*10^{11}m$

Let intensity at earth is .

11

Let the distance be r2 where intensity is double of that at earth, $I_{2}=2I_{1}$

Now, using (i) :

$\frac{I_{1}}{I_{2}}=\frac{r_{2}^{2}}{r_{1}^{2}}$

$\Rightarrow r_{2}^{2}=\frac{I_{1}}{I_{2}}*r_{1}^{2}$

$\Rightarrow r_{2}=\sqrt{\frac{I_{1}}{I_{2}}}*r_{1} = \sqrt{\frac{I_{1}}{2I_{1}}}*1.496*10^{11} = \frac{1.496*10^{11}}{\sqrt{2}}=1.06*10^{11}m$

Therefore, correct option is option b. [answer]