Question

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 nm and delivers 250 mW of power spread over a circular spot 510 μm 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 ms long, how much energy is delivered to the retina with each pulse? Express your answer with the appropriate units
B) What average pressure would the pulse of the laser beam exert at normal incidence on a surface in air if the beam is fully absorbed? Express your answer with the appropriate units.
C) What are the wavelength of the laser light inside the vitreous humor of the eye? Express your answer with the appropriate units.
D) What is the frequency of the laser light inside the vitreous humor of the eye? Express your answer with the appropriate units.
E) What is the maximum value of the electric field in the laser beam? Express your answer with the appropriate units.
F) What is the maximum value of the magnetic field in the laser beam?

Answer 1

Answer:

A)      E = 3.75 10⁻⁴ J , B) P = 1.25 10⁻¹² Pa, C)  λₙ = 604.48 10⁻⁹ m = 604 nm, D)    f = 3.7 10¹⁴ Hz , E)  E₀ = 2,148 10⁴ N /C, F)   B₀ = 7.16 10⁻⁹ T

 

Explanation:

Let's reduce the magnitudes to the SI system

           λ = 810 nm = 810 10⁻⁹ m

           P = 250 mW = 250 10⁻³ W = 0.250 W

           d = 510 um = 510 10⁻⁶ m

A) The power is defined

           P = W / t = E / t

           E = P t

           E = 0.250 1.50 10⁻³

           E = 3.75 10⁻⁴ J

B) The radiation pressure is

             P = E / c

             P = 3.75 10⁻⁴ / 3 10⁸

            P = 1.25 10⁻¹² Pa

C) the speed of light is given by

            c = λ f

The frequency does not change when moving from one medium to another, resonant processes, therefore to maintain the speed of light in the material medium we have

           v = λₙ f

We divide the two expressions

           c / v = λ / λₙ

Let's use

           n = c / v

           λₙ = λ / n

           λ = 810 10⁻⁹ / 1.34

           λₙ = 604.48 10⁻⁹ m

           λₙ = 604.48 nm

D) the passage of radiation from one medium to another is a resonant type process where the radiation excites the electrons that decay emitting at the same frequency

                      f = c / λ

                      f = 3 10⁸/810 10⁻⁹

                      f = 3.7 10¹⁴ Hz

E) In this part let's use the radiation intensity ratio

                   I = E₀² /μ₀ c

                  E₀ = √ I μ₀ c

Intensity is defined

                   I = P / A

In circle area is

                  A = π r² = π d² / 4

We replace

                  E₀ = √ (μ₀ c P 4/πd²)

                   E₀ = √ (4π 10⁻⁷  3 10⁸ 0.250 4 /π (510 10⁻⁶)²)

                   E₀ = √ 4.6136 10⁸

                   E₀ = 2,148 10⁴ N /C

F) to find the magnetic field let's use that the fields are in phase

                    c = E₀ / B₀

                    B₀ = E₀ / c

                    B₀ = 2,148 10⁴/3 10⁸

                    B₀ = 7.16 10⁻⁹ T