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 Iaser hits the spot.
A) 21.3 mW
B) 17.9 mW
C) 13.2 mW
D) 24.7 mW

Question

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 Iaser hits the spot.
A)  21.3 mW
B)  17.9 mW
C)  13.2 mW
D)  24.7 mW

Quizplus · Accepted Answer

To find the power output of the laser, we first calculate the area of the spot using the formula for the area of a circle, $A = \pi r^2$, where $r$ is the radius of the spot. Given the diameter is 1.31 mm, the radius is half of that, $r = 0.655$ mm or $0.655 \times 10^{-3}$ m. The area is then $A = \pi (0.655 \times 10^{-3})^2 = 1.346 \times 10^{-6}$ m$^2$. The power output of the laser, $P$, can be found by multiplying the intensity, $I$, by the area, $A$, so $P = I \times A = 1.58 \times 10^4 \times 1.346 \times 10^{-6} = 21.3$ 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 $1.58 \times 10 ^ { 4 } \mathrm {~W} / \mathrm { m } ^ { 2 }$