You get a summer internship working with a 589.2nm laser (an intense light source with a very well defined wavelength). You want to spray some oil with noil=1.25 on your glasses with nglass=1.50 as an additional safety feature to protect you from accidental flashes of laser light.Your applicator can only spray films thicker than 600nm. What is the thinnest film you can spray with the applicator given above that protects your eyes from the laser light beam?

Question

You get a summer internship working with a 589.2nm laser (an intense light source with a very well defined wavelength). You want to spray some oil with noil=1.25 on your glasses with nglass=1.50 as an additional safety feature to protect you from accidental flashes of laser light.Your applicator can only spray films thicker than 600nm. What is the thinnest film you can spray with the applicator given above that protects your eyes from the laser light beam?

Answer 1

To determine the thinnest film that can protect your eyes from the laser light, we need to consider the concept of interference. Interference occurs when two or more waves superpose (combine) to form a resultant wave.

In this case, the laser light passing through the oil film and the glass will undergo interference. The condition for constructive interference, where the waves reinforce each other, is given by the equation:

2nt = mλ

Where:
- n is the refractive index of the material
- t is the thickness of the film
- m is an integer representing the order of the interference
- λ is the wavelength of the laser light

We want to determine the thickness of the film (t) that will cause destructive interference (i.e., minimize the transmission of the laser light through the film).

Since the refractive index of the oil (noil) is 1.25 and the refractive index of the glass (nglass) is 1.50, we can use the equations:

nt = λ/4 for destructive interference (m = 1)
nt = 3λ/4 for destructive interference (m = 3)

Let's calculate the minimum thickness of the film in both cases:

For m = 1:
t1 = λ/(4n) = 589.2 nm / (4 * 1.25) = 118 nm

For m = 3:
t3 = 3λ/(4n) = 589.2 nm / (4 * 1.25) = 354 nm

Since the applicator can only spray films thicker than 600 nm, the thinnest film you can use to protect your eyes from the laser light beam is 600 nm.

Please note that this calculation assumes ideal conditions and does not consider factors such as the beam profile or scattering effects, which may have additional safety considerations. It is essential to consult with experts and follow appropriate safety guidelines when dealing with laser systems.