Light from a laser forms a 1.31-mm diameter spot on a wall. If the light intensity in the spot is $1.58 \times 10 ^ { 4 } \mathrm {~W} / \mathrm { m } ^ { 2 }$ what is the power output of the laser? Assume that all the light emitted by the laser hits the spot.

Question

Quizplus · Accepted Answer

The power output of the laser is equal to the intensity of the light in the spot multiplied by the area of the spot. The area of the spot is given by $\pi r^2$, where $r$ is the radius of the spot. The radius of the spot is half the diameter, so $r = 0.655 \mathrm {~mm} = 6.55 \times 10 ^ { -4 } \mathrm {~m}$. Therefore, the area of the spot is:$$A = \pi r^2 = \pi (6.55 \times 10 ^ { -4 } \mathrm {~m})^2 = 1.34 \times 10 ^ { -6 } \mathrm {~m}^2$$The power output of the laser is then:$$P = IA = (1.58 \times 10 ^ { 4 } \mathrm {~W} / \mathrm { m } ^ { 2 })(1.34 \times 10 ^ { -6 } \mathrm {~m}^2) = 21.3 \mathrm {~mW}$$

Light from a Laser Forms a 1 1.58×104 W/m21.58 \times 10 ^ { 4 } \mathrm {~W} / \mathrm { m } ^ { 2 }1.58×104 W/m2

Light from a Laser Forms a 1 $1.58 \times 10 ^ { 4 } \mathrm {~W} / \mathrm { m } ^ { 2 }$