The solid angle subtended by the periphery of an area `1cm^(2)` at a point situtated symmetrically at a distance of 5 cm from the area is

Options

A. `2xx10^(-2)` steradian
B. `4xx10^(-2)` steradian
C. `6xx10^(-2)` steradian
D. `8xx10^(-2)` steradian

Explanation

To solve the problem of finding the solid angle subtended by the periphery of an area of \(1 \, \text{cm}^2\) at a point situated symmetrically at a distance of \(5 \, \text{cm}\), we will use the formula for solid angle. Here are the steps:

### Step 1: Understand the Formula for Solid Angle
The solid angle \(\Omega\) (in steradians) subtended by an area \(A\) at a distance \(r\) is given by the formula:
\[ \Omega = \frac{A}{r^2} \]
where:
- \(A\) is the area in square centimeters,
- \(r\) is the distance from the area to the point in centimeters.

### Step 2: Identify the Given Values
From the problem, we have:
- Area \(A = 1 \, \text{cm}^2\)
- Distance \(r = 5 \, \text{cm}\)

### Step 3: Substitute the Values into the Formula
Now, we can substitute the values into the formula:
\[ \Omega = \frac{1 \, \text{cm}^2}{(5 \, \text{cm})^2} \]

### Step 4: Calculate the Denominator
Calculate \( (5 \, \text{cm})^2 \):
\[ (5 \, \text{cm})^2 = 25 \, \text{cm}^2 \]

### Step 5: Calculate the Solid Angle
Now substitute back into the equation:
\[ \Omega = \frac{1 \, \text{cm}^2}{25 \, \text{cm}^2} = \frac{1}{25} \]

### Step 6: Convert to Steradians
Since the unit of solid angle is steradians, we can express this as:
\[ \Omega = 0.04 \, \text{steradians} = 4 \times 10^{-2} \, \text{steradians} \]

### Final Answer
Thus, the solid angle subtended by the periphery of an area of \(1 \, \text{cm}^2\) at a distance of \(5 \, \text{cm}\) is:
\[ \Omega = 4 \times 10^{-2} \, \text{steradians} \]