There is a source of leaser beam whose power is 3 m W. Energy stored in 90 cm length of this laser beam is found to be ` n xx 10 ^(-12) J.` what is the value of n ?

Explanation

To find the value of \( n \) in the energy stored in a 90 cm length of a laser beam with a power of 3 mW, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Power to Watts:**
The power of the laser beam is given as 3 mW. We need to convert this to watts.
\[ P = 3 \, \text{mW} = 3 \times 10^{-3} \, \text{W} \]

2. **Convert Length to Meters:**
The length of the laser beam is given as 90 cm. We need to convert this to meters.
\[ L = 90 \, \text{cm} = 0.9 \, \text{m} \]

3. **Calculate the Time Taken to Travel 90 cm:**
The speed of light (or the speed of the laser beam) is approximately \( 3 \times 10^8 \, \text{m/s} \). We can calculate the time taken to travel 0.9 m using the formula:
\[ t = \frac{L}{v} = \frac{0.9 \, \text{m}}{3 \times 10^8 \, \text{m/s}} = 3 \times 10^{-9} \, \text{s} \]

4. **Calculate the Energy Stored:**
The energy stored in the laser beam can be calculated using the formula:
\[ E = P \times t \]
Substituting the values we have:
\[ E = (3 \times 10^{-3} \, \text{W}) \times (3 \times 10^{-9} \, \text{s}) = 9 \times 10^{-12} \, \text{J} \]

5. **Compare with Given Energy:**
The problem states that the energy stored is \( n \times 10^{-12} \, \text{J} \). From our calculation, we found:
\[ E = 9 \times 10^{-12} \, \text{J} \]
Therefore, we can equate:
\[ n \times 10^{-12} = 9 \times 10^{-12} \]
This gives us:
\[ n = 9 \]

### Final Answer:
The value of \( n \) is \( 9 \).

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