LASIK eye surgery uses pulses of laser light to shave off tissue ...

Question

LASIK eye surgery uses pulses of laser light to shave off tissue from the cornea, reshaping it. A typical LASIK laser emits a 1.0-mm-diameter laser beam with a wavelength of 193 nm. Each laser pulse lasts 15 ns and contains 1.0 mJ of light energy.b. During the very brief time of the pulse, what is the intensity of the light wave?

Accepted Answer

Hey, everyone in this problem, we're told that lasers high precision welding features make them suitable to weld implantable medical devices. OK. The typical laser used during this process operates at a wavelength of 1064 nanometers with a typical pulse duration of five nanoseconds. Each laser pulse contains two jewels. The laser spot radius is 0.75 millimeters. And we're asked to calculate the intensity of the laser pulse. We're given four answer choices all in watts per meter squared. Option A 7.1 times 10 to the exponent two, option B 2.3 times 10 to the exponent five, option C 7.1 times 10 to the exponent 11 and option D 2.3 times 10 to the exponent 40. So what we're gonna do is we're just gonna go through and write down everything we've been given in this problem. OK. We were given a lot of value. So let's write them out so we can keep track. So the first thing we were given is the wavelength and we're gonna call that lambda and that is 1064 nanometers. OK. Next, we were given the time tea of five nanoseconds, we're told that each pulse contains two jewels. OK. We're talking about jewels. So we're talking about energy. So each pulse is gonna have an energy E equal to two jewels. And finally, we're told the radius of the laser spot which we'll call R is 0.75 millimeters. Now we're looking for the intensity of the laser pulse. OK. So recall that the intensity of something can be written I is equal to the power P divided by the area. Yeah, the laser spot. And we know that's gonna be a circle, we have its radius so we can calculate the area. But we need the power P in order to determine what our intensity is going to be, right? So let's now look at the power P. OK. And the power P recall it's gonna be equal to the energy divided by the time we know the energy, we know the time. So we can calculate our power P substitute it back into our intensity equation and solve for the intensity like we want now our final unit. OK. And the answer choices is in watts per meter squared. So we want to go ahead and convert all the values that we're gonna be using into their standard units. OK. What you'll see is that the wavelength is actually not used in this calculation. So we don't have to worry about that. We are gonna use the time. OK. So we have nanoseconds to go from nanoseconds to seconds. We're gonna use times 10 to the exponent negative nine. And so this becomes five times 10 to the exponent negative nine seconds. The energy to Jews, that's already in the standard unit. That's great. And then our radius, it's in millimeters, we wanna convert to meters. So we're gonna divide by 1000, then we get 7.5 times 10 to the exponent negative 4 m. All right. So looking at our power equation with our standard units, now we have that the power is gonna be the energy divided by the time which in this case is going to be two Jews divided by five times 10 to the exponent negative nine seconds. This is gonna give us the power of four times 10 to the exponent eight. We have jewels per second which is equivalent to a watt. OK? So we have our power Penna, we can use that in our intensity equation. We just need the area as well. OK. So let's calculate the area as well. And we know that the area because we have a circle is going to be pi multiplied by R squared. So in our intensity equation now we have that I is equal to the power four times 10 to the exponent eight watts divided by pi multiplied by the radius 7.5 times 10 to the exponent negative 4 m all squared. And if we work this out on our calculator, we get an intensity of about 2. 354 times 10 to the exponent 14 watts per meter squared. And that is that fine value that the question was asking for? If we compare this to the answer choices we were given. Ok. We're gonna round to two significant digits. We can see that the correct answer is option D 2.3 times 10 to the exponent 14 watts per meter squared. Thanks everyone for watching. I hope this video helped see you in the next one.

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