Question

A 15.0-mW helium-neon laser emits a beam of circular cross section with a diameter of 2.00mm. (b) What total energy is contained in a 1.00-\mathrm{m} length of the beam?

Answer 1

To find the total energy in a 1.00 m length of the beam, we calculate the area of the circular cross section of the beam and then multiply it by the energy per unit length.

Step-by-step explanation:

To calculate the total energy contained in a 1.00 m length of the beam, we first need to find the area of the circular cross section of the beam. The diameter of the beam is given as 2.00 mm, so the radius is 1.00 mm. Using the formula for the area of a circle, A = πr², we can calculate the area as A = π(1.00 mm)².

Next, we need to calculate the energy per unit length of the beam. The power output of the laser is given as 15.0 mW, so the energy per unit length is simply the power divided by the length, which is 15.0 mJ/m.

Finally, we can calculate the total energy in a 1.00 m length of the beam by multiplying the energy per unit length by the length, which is (15.0 mJ/m) × 1.00 m = 15.0 mJ.

Answer 2

The total energy in a 1.00-meter length of a 15.0-mW helium-neon laser beam with a 2.00 mm diameter is calculated using the power of the laser and the time it takes for light to travel 1.00 meter. The resulting energy is 5.00 × 10−5 joules.

Step-by-step explanation:

The question asks about the total energy contained in a 1.00-meter length of a helium-neon laser beam with a power of 15.0 mW and a diameter of 2.00 mm. To find the total energy, we need to use the relationship between power (P), energy (E), and time (t), which is P = E/t. Since power is the rate at which energy is transferred, we can calculate the total energy by rearranging the formula to E = P × t.

In this case, the length of time the laser is on is the time it takes for the light to travel 1.00 m. Given that the speed of light is approximately 3.00 × 108 m/s, we can calculate the time:

t = Δd / c = 1.00 m / (3.00 × 108 m/s) = 3.33 × 10−6 s

Now, using the given power of the laser:

E = P × t = 15.0 × 10−3 W × 3.33 × 10−6 s = 5.00 × 10−5 J

Hence, the total energy contained in a 1.00-meter length of the laser beam is 5.00 × 10−5 joules.