A narrow ray of yellow light from glowing sodium (λ0=589 nm) traveling in air strikes a smooth s

A narrow ray of yellow light from glowing sodium (λ0=589 nm)...

A narrow ray of yellow light from glowing sodium $\left(\lambda_{0}=589 \mathrm{nm}\right)$ traveling in air strikes a smooth surface of water at an angle of $\theta_{i}=35.0^{\circ} .$ Determine the angle of refraction, $\theta_{r}$

Key Concepts

Refractive Index

The refractive index is a measure of how much a material slows down light compared to the speed of light in a vacuum. It plays a critical role in determining how much light bends when it enters a different medium, as a higher refractive index indicates a greater reduction in speed and thus a greater degree of bending.

Snell's Law

Snell's Law provides the quantitative relationship between the angles of incidence and refraction and the indices of refraction of the two media. It is expressed as n? sin(??) = n? sin(??), where n? and n? are the refractive indices of the first and second media, and ?? and ?? are the angles of incidence and refraction, respectively.

Refraction

Refraction is the bending of light as it passes from one medium to another with a different optical density. This phenomenon occurs because light travels at different speeds in different media, leading to a change in direction at the interface between the two materials.

Transcript

00:01 How's going everybody? so in this problem, what we're trying to calculate is the angle of refraction.

00:07 All of you guys have taken a pencil and have put it into a clear cup of water or any sort of object, and you notice that it bends when it goes in the water.

00:16 So this happens because of the process of refraction.

00:19 So what we're trying to do is calculate what that angle of refraction is.

00:24 In physics, whenever you come across problems that ask you to calculate index of refractions or angles of refractions or angles of incident, you always use the same formula.

00:36 It's called snell's law.

00:39 So what it says is you take the index of refraction of the first medium, multiply it by sign of the incident angle, okay, the first angle, so the angle that the light ray hits the water at in this problem, and you set that equal to the index of refraction of the second material.

01:01 So in this problem would be water.

01:03 And then you multiply it by sign of the angle of refraction.

01:11 So in this problem, we can look up what the index of refraction of air is.

01:17 We can look up what the index of refraction of water is, and we're given that the incident angle is 35 degrees.

01:25 So we know what n1 is.

01:27 We know what theta i is.

01:29 We know what n2 is.

01:31 We just need to be able, we just have to be able to calculate what this is.

01:35 So let's go ahead and do that.

01:37 After plugging in what we know.

01:39 So you can look up that the index of refraction of air, which is the first medium, it's where the light ray starts, is one.

01:48 And we're given in the problem that the incident angle is 35 degrees.

01:57 You can also look up that the index of refraction of water is 1 .33.

02:03 It's a tabulated value.

02:06 I guess they just didn't want to put it in the book, and the problem, i guess.

02:10 So then we're going to multiply by sign, of the angle of refraction.

02:17 Okay? so what we're ultimately going to want to do in this problem is we're going to want to get this theta r by itself...

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