Question

The solid angle subtended by the periphery of square of side $5\text{cm}$ at a point situated symmetrically at a distance of $10\text{cm}$ from the square is :

• A. $0.5\text{steradian}$
• B. $0.25\text{steradian}$
• C. $1\text{steradian}$
• D. $1.5\text{steradian}$

Answer 1

The correct option is B $0.25\text{steradian}$

Given data,
Side of the square $a=5\text{cm}$
Distance $=10\text{cm}$
Solid angle $\Omega =?$

Area of the square is given by,
$A=a^2=5\times 5=25{\text{cm}}^2$

We know the formula,
Solid angle $\Omega =\frac{\text{Area}}{{\text{(Radial distance)}}^2}$

$\Omega =\frac{25}{{10}^2}=\frac{1}{4}$

$\Rightarrow \Omega =0.25\text{steradian}$