Light enters a solid pipe made of plastic having an index of...

Light enters a solid pipe made of plastic having an index of refraction of 1.60. The light travels parallel to the upper part of the pipe ($\textbf{Fig. E33.15}$). You want to cut the face $AB$ so that all the light will reflect back into the pipe after it first strikes that face. (a) What is the largest that $\theta$ can be if the pipe is in air? (b) If the pipe is immersed in water of refractive index 1.33, what is the largest that $\theta$ can be?

Key Concepts

Critical Angle

The critical angle is the minimum angle of incidence, measured from the normal, above which total internal reflection occurs when light travels from a denser medium to a less dense medium. It can be calculated using the formula sin?_c = n?/n?, where n? is the index of refraction of the denser medium and n? is that of the less dense medium. This concept is essential for understanding and predicting the conditions needed for complete internal reflection of light.

Snell's Law

Snell's Law describes the relationship between the angles of incidence and refraction when light passes 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 of the initial and secondary media, respectively, and ?? and ?? are the corresponding angles with respect to the normal.

Index of Refraction

The index of refraction is a measure of how much light slows down when traveling through a medium compared to vacuum. It determines the degree of bending (refraction) of a light ray at the interface between two different media, and it plays a central role in all calculations involving light propagation, reflection, and refraction.

Total Internal Reflection

Total internal reflection is a phenomenon that occurs when light traveling from a medium with a higher index of refraction to one with a lower index of refraction strikes the interface at an angle greater than a specific critical value. Under these conditions, the light does not refract into the second medium but is entirely reflected back into the first medium, which is key in designing optical systems such as fiber optics.

Transcript

00:02 All right, so we have a question about critical angle here.

00:05 We're given the scenario where we have a plastic pipe with an index refraction of 1 .6, and we want to know how, what angle do we need to cut this pipe in order to remain or have the light do a complete internal reflection.

00:23 And that's what the critical angle is measuring.

00:25 So the critical angle equation is inverse sign of the, where it's headed, which would be the air's index and refraction in this first question, divided by where it was in one.

00:42 So that would be plastic.

00:43 So that's oftentimes where students will confuse which one is what.

00:48 We're seeing this in terms of this is in one here.

00:52 And if we make a cut, it's going to go into either water or air, that would be an n2.

01:01 And what happens when the critical angle is matched is that the light rays are essentially traps.

01:09 They follow along on the actual angle if we cut it just right and they won't escape.

01:18 There will be no light traveling out of this transparent material.

01:24 So let's try this equation here and see what we get for the two scenarios.

01:31 So our first scenario we're looking at in terms of going from plastic to air.

01:36 So that's going to be inverse sign of what we were in we were in we were in plastic but we're going to go into we're trying to go into the air so we can do this ratio.

01:58 If we did the opposite ratio we'd get an air on calculating this so we can't have a number of so 1 divided by 1 .6, and then we're going to take the inverse sign of that.

02:12 Make sure that you're in degrees for this.

02:16 So i get 38 .68.

02:20 So we're going to round this to three significant figures because our index and refractions we're in that.

02:27 So 38 .7 degrees is our first answer.

02:33 And then part b, we're going to do the same thing, except now we're going to do the same thing, except now we're we have a different ratio here.

02:40 We have it trying to go in through water and we're dividing that by 1 .6, 1 .33 by 1 .6 and then we take the inverse sign of that.

03:01 8, 3 ,1 ,25, and you get a 56 to be, 56 .2 ,7, so i'm going to round that to two digits again.

03:13 So for three digits, i apologize.

03:16 56 .2 degrees...

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