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$\bullet$ A researcher measures the thickness of a layer of benzene$(n=1.50)$ floating on water by shining monochromatic lightonto the film and varying the wavelength of the light. She findsthat light of wavelength 575 nm is reflected most stronglyfrom the film. What does she calculate for the minimum thick-ness of the film?
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The minimum thickness of the benzene that would strongly reflect 575 nm wavelength of light is $95.8 nm .$
Physics 102 Electricity and Magnetism
Interference and Diffraction
Reflection and Refraction of Light
Simon Fraser University
University of Sheffield
University of Winnipeg
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.
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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already. This problem is another thin film problem. So in this case, we have our air never water. They don't give us the index of refraction, but it's used often enough that you can either remember or look it up that it's 1.33 and we're looking at a Cine film of benzene, which is 1.5. All right, so let's trace our path of light to figure out what our phase changes we're gonna be. So we're going from low to high end. Sarin is increasing, which means we d'oh, get a face change there, blink. And now we're going from high to low. And so and it's decreasing. So there's no phase change here. So write out the bet are two beams that we end with are out of phase. So right now they're destructively interfering. But this question wants to know where is it the most brightly reflected. So we're looking for constructive interference there, which means we need to cancel out this phase change by exploiting the condition in here. So the thickness of my film is T. I want to make sure that won t to t of that past length shift that these were getting is going to cancel out that phase shift we got from reflecting. So instead of being an integer multiple, I love the wavelength. It's going to be integer and 1/2 multiple off the wavelength in the film. All right, so remember that wave, like inside the film is the wavelength outside an heir divided by the index of refraction. So if I stick that in there, I get to t is equal to m plus 1/2 lambda zero over. And if I saw for tea, you get them plus 1/2 Lambda zero over to and Mary. Now we're looking for the minimum. So that's going to occur when M is equal to zero. Okay, now, if I plug in my numbers, T is gonna be 1/2 Lambda Zero was the wavelength that she shined on it in air just 5 75 centimeters right by two. And n is end of my film. So that's going to be 1.5. If I plug lead into my handy dandy calculator, I get 95 point eat. Yeah, the meter's
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