Find energy stored in a 30 cm length of a laser beam operating at 6 mW.

Answer

To find the energy stored in a 30 cm length of a laser beam operating at 6 mW, we can follow these steps:

### Step 1: Convert the Length to Meters
The length of the laser beam is given as 30 cm. We need to convert this to meters.
\[ \text{Length} = 30 \, \text{cm} = 30 \times 10^{-2} \, \text{m} = 0.30 \, \text{m} \]

### Step 2: Determine the Speed of Light
The speed of light in a vacuum is a constant:
\[ c = 3 \times 10^8 \, \text{m/s} \]

### Step 3: Calculate the Time Taken for the Laser Beam
To find the time taken for the laser beam to travel the length of 30 cm, we use the formula:
\[ \text{Time} = \frac{\text{Length}}{\text{Speed}} = \frac{0.30 \, \text{m}}{3 \times 10^8 \, \text{m/s}} \]
Calculating this gives:
\[ \text{Time} = 1 \times 10^{-9} \, \text{s} \]

### Step 4: Convert Power to Watts
The power of the laser beam is given as 6 mW. We need to convert this to watts:
\[ \text{Power} = 6 \, \text{mW} = 6 \times 10^{-3} \, \text{W} \]

### Step 5: Calculate the Energy Stored
Using the formula for energy, which is the product of power and time:
\[ \text{Energy} = \text{Power} \times \text{Time} \]
Substituting the values we have:
\[ \text{Energy} = (6 \times 10^{-3} \, \text{W}) \times (1 \times 10^{-9} \, \text{s}) = 6 \times 10^{-12} \, \text{J} \]

### Final Answer
The energy stored in the 30 cm length of the laser beam operating at 6 mW is:
\[ \text{Energy} = 6 \times 10^{-12} \, \text{J} \]

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