Three sheets of plastic have unknown indices of refraction....

Three sheets of plastic have unknown indices of refraction. Sheet 1 is placed on top of sheet $2,$ and a laser beam is directed onto the sheets from above so that it strikes the interface at an angle of $26.5^{\circ}$ with the normal. The refracted beam in sheet 2 makes an angle of $31.7^{\circ}$ with the normal. The experiment is repeated with sheet 3 on top of sheet $2,$ and, with the same angle of incidence, the refracted beam makes an angle of $36.7^{\circ}$ with the normal. If the experiment is repeated again with sheet 1 on top of sheet $3,$ what is the expected angle of refraction in sheet 3? Assume the same angle of incidence.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Sequential Refraction in Multi-layer Systems

When light passes through multiple layers of materials with different refractive indices, it undergoes refraction at each interface as dictated by Snell's Law. Understanding how to apply Snell's Law sequentially is key in analyzing experiments and predicting the final direction of the light beam after passing through several media.

Index of Refraction

The index of refraction is a measure of how much light bends, or refracts, when it enters a material. It quantifies the ratio of the speed of light in a vacuum to the speed of light in the material and is fundamental in determining how light propagates through different media.

Snell's Law

Snell's Law is the principle governing the relationship between the angles of incidence and refraction when light passes from one medium to another. It is represented mathematically as n? sin(??) = n? sin(??), where n? and n? are the indices of refraction of the two media, and ?? and ?? are the angles relative to the normal. This law is essential for analyzing and predicting how light bends at interfaces.

Transcript

00:01 So we are being asked.

00:02 We're told that we have a light passing through sheet 1 at an angle of 26 .5 degrees.

00:09 It's a sheet 1.

00:12 And it's passing into sheet 2 with a refraction angle of 31 .7 degrees.

00:20 Now we're doing the same thing with sheet 3 at the same angle of incident.

00:25 So we have 26 .5 degrees.

00:27 And it's going into sheet 2 and giving us an angle of refraction of 36 .7 degrees.

00:36 Finally, we are being asked if sheet 1 is as the same angle of incidence as the previous 2, what will be the angle of refraction if it were to go into sheet 3? so the question that we have to ask ourselves is we look at this.

01:00 And you have to say that if n1, sign of theta 1 is equal to n3 sign of theta 3, in order to find sine of theta 3, in order to find theta 3, we need to know what the ratio of n1 to n3 is.

01:20 So here we can find out what the ratio of n2 to n3 is, and here we can find out what the ratio of n2 to n3 is, to n2 is.

01:35 So if we take these two and we combine them, we can get the ratio.

01:41 So if we multiply these two together, n1 times n2 over n2, n1 over n2 times n2 over n3 should give us n1 over m3.

01:54 So we want to find out what that ratio is.

01:58 So we're going to do that.

02:00 We're going to find both of these ratios...

Please give Ace some feedback