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 of the laser beam to meters
The length of the laser beam is given as 30 cm. We need to convert this to meters for consistency in units.

\[ \text{Length} (L) = 30 \text{ cm} = 0.30 \text{ m} \]

### Step 2: Identify the power of the laser beam
The power of the laser beam is given as 6 mW. We need to convert this to watts.

\[ \text{Power} (P) = 6 \text{ mW} = 6 \times 10^{-3} \text{ W} \]

### Step 3: Calculate the time taken for light to travel the length of the beam
The speed of light (c) is approximately \(3 \times 10^8 \text{ m/s}\). We can use the formula:

\[ t = \frac{L}{c} \]

Substituting the values:

\[ t = \frac{0.30 \text{ m}}{3 \times 10^8 \text{ m/s}} = 1 \times 10^{-9} \text{ s} \]

### Step 4: Calculate the energy stored in the laser beam
The energy (E) stored in the laser beam can be calculated using the formula:

\[ E = P \times t \]

Substituting the values we have:

\[ E = (6 \times 10^{-3} \text{ W}) \times (1 \times 10^{-9} \text{ s}) = 6 \times 10^{-12} \text{ J} \]

### Final Answer
The energy stored in a 30 cm length of a laser beam operating at 6 mW is:

\[ E = 6 \times 10^{-12} \text{ J} \]

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