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$\bullet$$\bullet$ Laser surgery. Very short pulses of high-intensity laser beams are used to repair detached portions of the retina of the eye. The brief pulses of energy absorbed by the retina welds the detached portion back into place. In one such procedure, a laser beam has a wavelength of 810 $\mathrm{nm}$ and delivers 250 $\mathrm{mW}$ of power spread over a circular spot 510$\mu \mathrm{m}$ in diameter. The vitreous humor (the transparent fluid that fills most of the eye) has an index of refraction of 1.34 . (a) If the laser pulses are each 1.50 $\mathrm{ms}$ long, how much energy is delivered to the retina with each pulse? (b) What average pressure does the pulse of the laser beam exert on the retina as it is fully absorbed by the circular spot? (c) What are the wavelength and frequency of the laser light inside the vitreous humor of the eye? (d) What are the maximum values of the electric and magnetic fields in the laser beam?

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a) 0.375 $\mathrm{mJ}$b) $4.077 \times 10^{-3} \mathrm{N} / \mathrm{m}^{2}$ or $4.077 \times 10^{-3} \mathrm{Pa}$c) 604.5 $\mathrm{nm}$d) $3.033 \times 10^{4} \mathrm{V} / \mathrm{m}$$1.011 \times 10^{-4} \mathrm{T}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 23

Electromagnetic Waves and Propagationof Light

Electromagnetic Waves

Reflection and Refraction of Light

Cornell University

Rutgers, The State University of New Jersey

University of Washington

University of Winnipeg

Lectures

02:30

In optics, ray optics is a geometric optics method that uses ray tracing to model the propagation of light through an optical system. As in all geometric optics methods, the ray optics model assumes that light travels in straight lines and that the index of refraction of the optical material remains constant throughout the system.

10:00

In optics, reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Reflection may also be referred to as "mirror image" or "specular reflection". Refraction is the change in direction of a wave due to a change in its speed. The refractive index of a material is a measure of its ability to change the direction of a wave. A material with a higher refractive index will change the direction of a wave to a greater degree than a material with a lower refractive index. When a wave crosses the boundary between two materials with different refractive indices, part of the wave is refracted; that is, it changes direction. The ratio of the speeds of propagation of the two waves determines the angle of refraction, which is the angle between the direction of the incident and the refractive rays.

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In the first part of this problem, we are going to calculate the energy delivered to the retina in each pulse. We call this energy e, as he is written as equals to p multiplied by t. Well, the p is the power delivered to the potina, and t is the time taken. So we call this question as equation number 1. Now, by inserting the values into this question, we can write it is equals to. We have the value for p as 250 multiplied with the rasper minus 3. What and then we have the time as 1.50 multiplied with 10 rate power minus 3 seconds, so this will give us. The value for e is equals to 0.375 multiplied by 10. This power minus 3 joule, so it can be written as a equals to 0.375 millisol. So this is the required answer now. In part b of this problem, we have to calculate the average pressure exerted by the pulse on retina, so this pressure is written as a p average and the pressure is defined as a p f equals to i divided by c, where the i is the intensity Of the pulse and we see a speed of light in vacuum, we call this equation as equation number 2. We can write the intensity as intensity goes to power divided by area, and in this case we have. The area is pi r square. Now inserting the value of this area into this equation, and then the value of this i back into equation number 2. We can write the equation: number 2 s p over equal to p, divided by pi r square c. Now, in setting values into the square, we can write it as per equals. 2. We have. The value for bar is 250 multiplied by 10 is minus 3. What divided by we have 3.14 into, we have. The value for r is 255 multiplied by 10 power. Minus 6 meter square, and then we have the value for c as 3.0 multiplied by 10 in the power 8 meter per second. So this will give us a value for pressure of a pet pressure, as p is equal to 4.08 multiplied by 10 at power. Minus 3 pascal, so this is the answer now in part c of this problem. We have to calculate the length and frequency of this beam inside the ee, so we call the wavelength, has lambda e and a frequency has f e. This is the part c of this problem. We can write lambda e as lambda equals to lambda divided by n. What is lambda is the enof that beam in vacuum and n is the reflection of the material inside the ee o by setting the values into the we can write. It is. This is equal to 810 nanometer divided by. We have the reflecting is 1.34, so this will give the value for lambda lambda equals to 624 nanometer. So this is the answer. Similarly, we can write the relation for this f e, as f equals to cor lambda. This can be written as a v divided by lambda e. We, this is the speed of light in that medium. When setting values for the c and lambda, we can write it as f equals to equals to. We have the value for c s: 3.0 multiplied by 10 power 8 meter per second divided by this lambda is given by 810 multiplied with the ither minus 9 meter. So this will give us a value for this frequency, as f equals to 3.70 multiply with them. Is the power fourty nets? So this is the answer now in part of this problem. We have to calculate the maximum value of lexic and minuti joels. That'S what we call e not and b, not so in order to calculate the stalactic field, we write the relation for intensity of the beam as equals to 1 over 2 epsilon, not c and e not square. Only this question for a not we can write it as e not equals to 2. I divided by epsilon, naught and c. Then we have a square out here. We call this equation as equation. Number 4. Now, by inserting values into this question we can write. It is not equal to square root of 2 multiplied by. We have the value, for. I is 1.22 multiplied by 10 inch power. Minus 2 is the power plus 6 watch per meter square is divided by. We have the value for epsilon, not as a 8.85 multiply with 10 raised power, minus 12 coulomb square per newton meters squared and then we have the value for c as 3.0 multiplied with his power 8 meter. So this is the square root up to this point. So this will give us a value for not as e not equals to 3.033 multiplied by turns power, 4 volt per meter. So this is the answer. Now we can write the relation for b as b. Is the magnetic field amplitude of minetic field e, not divided by cwyinserting values into the square we can write. It is 3.033 multiplied by 10 as power 4 volt per meter divided by divided by 3.0, multiplied by 10 rats power 8 meter per second. So this will get the value for this b, not as b not equals to 1.01 multiplied by 10 is power minus 4 tesla. So this is the required answer. Thank you.

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