Figure P 22.59 shows the path of a beam of light through...

Figure $\mathrm{P} 22.59$ shows the path of a beam of light through several layers with different indices of refraction. (a) If $\theta_{1}=30.0^{\circ}$, what is the angle $\theta_{2}$ of the emerging beam? (b) What must the incident angle $\theta_{1}$ be to have total internal reflection at the surface between the medium with $n=1.20$ and the medium with $n=1.00$ ?

Figure $\mathrm{P} 22.59$ shows the path of a beam of light through several layers with different indices of refraction. (a) If $\theta_{1}=30.0^{\circ}$, what is the angle $\theta_{2}$ of the emerging beam?
(b) What must the incident angle $\theta_{1}$ be to have total internal reflection at the surface between the medium with $n=1.20$ and the medium with $n=1.00$ ?

Key Concepts

Snell's Law

Snell's Law relates the angle of incidence and the angle of refraction when a wave, such as light, passes through the interface between two media with different indices of refraction. It is expressed as n?*sin(??) = n?*sin(??), where n? and n? are the indices of refraction, and ?? and ?? are the angles of incidence and refraction, respectively.

Index of Refraction

The index of refraction is a property of a medium that indicates how much light slows down when passing through it relative to its speed in a vacuum. This property is crucial for determining the degree to which light bends or refracts when it transitions between different materials.

Critical Angle

The critical angle is defined as the specific angle of incidence at which light traveling from a medium with a higher index of refraction to a lower index is refracted at 90 degrees along the boundary. Beyond this angle, total internal reflection occurs, meaning the light does not pass into the second medium.

Total Internal Reflection

Total internal reflection is the phenomenon that occurs when a light ray strikes the boundary of a medium at an angle greater than the critical angle, causing the light to be completely reflected back into the original medium rather than refracting into the second medium.

Transcript

0:00 Hi there.

00:01 So for this problem, we have this figure that shows the path of a beam of light through several layers of different index of refraption.

00:09 So for part a of this problem, we are told that the angle theta incidence theta 1 is equal to 30 degrees.

00:20 And so what we need to determine is the angle theta 2 of the emerging beam.

00:27 We need to determine the angle theta 2.

00:31 So what we are going to do is to apply snell's law at points a, b, and c.

00:40 These points in here, we're going to call this point a, this point b, and this point c.

00:49 So if we do that, we are going to obtain three equations.

00:53 So the first one is we're going to call this angle in here, alpha, this angle in here, b, and yes, that's it.

01:10 So we're going to have, the first equation is from passing of this one of index of refraction 1 .6 to this one of index of refruption 1 .4.

01:24 So we're kind of the following equation from this nell's law is going to be 1 .4 sine of alpha is equal to 1 .6.

01:39 Sine of theta 1.

01:44 That is the first equation for passing from this first layer.

01:50 So now we are in the position b.

01:54 Now we are coming from the index of refraption 1 .4 to the index of refraption 1 .2.

02:01 So in this case, the snl's law will give us 1 .2 sine of beta is equal to 1 .1 .2.

02:11 1 .4, sine of alpha.

02:16 And the final equation is for the point c, where we are going to have 1 for the last medium, because it is er, sine of theta 2.

02:32 And this is equal to the index of refraption n, that is the 1 root 4, which is 1 .2, sine of beta...

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