A Q A light ray of wavelength 589 nm is incident at an angle θon the top surface of a block of p

A Q A light ray of wavelength 589 nm is incident at an angle...

A $Q$ A light ray of wavelength 589 $\mathrm{nm}$ is incident at an angle $\theta$ on the top surface of a block of polystyrene as shown in Figure $\mathrm{P} 35.53$ . (a) Find the maximum value of $\theta$ for which the refracted ray undergoes total internal reflection at the left vertical face of the block. What If? Repeat the calculation for the case in which the polystyrene block is immersed in (b) water and (c) carbon disulfide. You will need to explain your answers.

A $Q$ A light ray of wavelength 589 $\mathrm{nm}$ is incident at an angle $\theta$ on the top surface of a block of polystyrene as shown in Figure $\mathrm{P} 35.53$ . (a) Find the maximum value of $\theta$ for which the refracted ray undergoes total internal reflection at the left vertical face of the block. What If?
Repeat the calculation for the case in which the polystyrene block is immersed in (b) water and (c) carbon disulfide. You will need to explain your answers.

Key Concepts

Snell's Law

Snell's Law is a fundamental principle in optics that describes how light rays change direction when they pass from one medium to another. It relates the angles of incidence and refraction to the refractive indices of the two media, allowing prediction of the light's path at an interface. This principle is critical in understanding how light behaves when crossing boundaries between different materials.

Refractive Index

The refractive index of a medium is a measure of how much the speed of light is reduced inside the medium compared to its speed in a vacuum. It indicates how strongly light is bent, or refracted, when entering the medium. This property plays a crucial role in determining the behavior of light at interfaces, especially in calculations involving refraction and reflection.

Critical Angle

The critical angle is the minimum angle of incidence for which total internal reflection occurs when light travels from a medium with a higher refractive index to one with a lower refractive index. Beyond this angle, all the light is reflected back into the original medium rather than being refracted. Understanding the critical angle is essential for analyzing conditions under which total internal reflection happens.

Total Internal Reflection

Total internal reflection is an optical phenomenon that occurs when a light ray traveling in a medium with a higher refractive index strikes the interface with a medium of lower refractive index at an angle greater than the critical angle. At this condition, no light is transmitted into the second medium; instead, it is completely reflected back into the first medium. This concept is key in applications such as fiber optics and optical devices.

Effect of the Surrounding Medium

The surrounding medium's refractive index significantly influences the conditions for total internal reflection because it alters the refractive index contrast at the interface. Changing the external medium involves recalculating the critical angle using the new refractive index, which directly affects whether and how total internal reflection can occur. This concept is important when analyzing scenarios where an optical material is immersed in different substances.

Transcript

00:01 To find out what the max what the theta value is into the polystyrene block that will cause total internal reflection or what the maximum angle is so let's evaluate this we know that the sign of theta c the critical angle is n2 over n1 so if we have a light ray moving from polystyrene in outside air, this would become one.

00:35 Well first let's just rearrange this.

00:37 We know that theta c is going to be the inverse sign of n2 over n1.

00:43 So if this is air and this is polystyrene, then we're going to have a critical angle of the following.

01:00 And that becomes 42 .155 degrees.

01:17 So next thing we're going to do is we are going to, now that we know the critical angle, we know that that's the same angle as the theta 2 when the light rate enters the polystyrene block.

01:29 So we're going to set up the following equation.

01:32 We're going to say n1, sine theta 1 is equal to n2, sine theta 2.

01:41 We will cross off n1, no, because the outside medium is air.

01:48 And to find theta 1, we will simply have to find the inverse.

01:51 Sign of n2, which is polystyrene, times a sign of theta 2, which we know is 42 .155.

02:10 And that will give us a theta 1 of 90 degrees, which means that for any angle of entry, it will cause total internal reflection inside the polystyrene.

02:22 So that is the answer to a.

02:24 We will now follow a similar process to find the answers to b and c.

02:30 So theta c for b will be sine negative 1, or the inverse sign of.

02:36 Instead of 1 on top, it's going to be water, so it's going to be 1 .333 over 1 .49, which is equal to 63 degrees.

02:53 So now we have 63 degrees.

02:55 We're going to plug that into this equation...

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