When the light illustrated in Figure P 35.21 passes through the glass block, it is shifted later

When the light illustrated in Figure P 35.21 passes through...

Key Concepts

Refraction

Refraction is the bending of a light ray when it passes from one medium into another with a different optical density. This bending occurs because light travels at different speeds in different media, which alters the direction of the light ray. It is a fundamental concept in optics used to understand how light behaves as it transitions between materials such as air and glass.

Snell's Law

Snell’s Law quantitatively describes the relationship between the angles of incidence and refraction when light crosses the boundary between two media with differing refractive indices. This law, expressed as n? sin?? = n? sin??, is essential for calculating the change in the light’s direction and is directly applied in determining the lateral displacement within the glass block.

Lateral Displacement

Lateral displacement refers to the sideways shift experienced by a light ray as it passes through a medium, such as a glass block, with parallel faces. Although the ray exits the medium parallel to its original direction, it is shifted laterally relative to its initial path, an effect that is intrinsically linked to the geometry of the light path and the refraction process.

Index of Refraction

The index of refraction is a measure of how much a medium slows down light relative to its speed in a vacuum. It is a crucial parameter in the calculation of refraction and lateral displacement, as it directly influences the degree of bending experienced by the light when entering or exiting a medium like glass.

Geometrical Analysis of Light Paths

The geometrical analysis of light paths involves using trigonometry and the principles of refraction to derive relationships between the physical parameters of the system, such as the thickness of the glass and the angles of incidence and refraction. This analysis is key to calculating the lateral shift of the light beam as it passes through the glass block.

Transcript

00:01 So we are told that a light beam is incident upon some glass, right? and that the glass is two centimeters thick.

00:16 So it is refracted at a certain angle, and we're going to call that angle theta.

00:27 And since, and the angle between the horizontal and this line, which is the light beam if it were to continue on, at its original angle is also 30 degrees.

00:44 So we want to find this distance d.

00:48 So how are we going to find d? well, if we view this guy as a right triangle for a second, we view this as a right triangle, with this being the 90 degree angle, and this being the 30 degree angle, we can find this distance, which we're going to call x, and subtract this distance, which we're going to call y, to find d.

01:21 So to find, we need to find out what this angle theta is in order to find out what y is.

01:29 So let's get to business doing that.

01:35 The first thing we're going to note is that the n of the glass is given to us and it is 1 .5.

01:50 So if, so the equation we're going to use is, bear with me here, the sine, n1, sine theta of 1 is equal to n2 sine theta of 2.

02:09 So n2 in this case is n of glass, and n1 we're going to assume as 1.

02:15 Because if it's air or a vacuum, it's going to be around about it.

02:19 So our angle, our angle theta 2 is what we are looking for.

02:26 So to solve for theta 2, we are going to find the inverse sine of sine of theta of 1 over n2.

02:37 So that is going to be a sign of 30 over 1 .5, which is going to give us an angle of, bear with me here, 19 .5 degrees.

03:12 So if we want to find this distance here, y, we are going to be able to do that by setting it equal to.

03:25 Okay.

03:26 So the first thing we're going to notice is that the cosine, let's say that the distance from this part of the glass of this right here is d.

03:37 So d, we already have a d, let's call this a.

03:41 So a times the cosine of theta 2 is equal to 2, right? because it's in this part of the triangle.

03:55 So to find a, we are going to say that a is equal to 2 divided by cosine of 19 .5, which is theta 2.

04:05 That means that a is equal to 2 .12 centimeters.

04:19 So if a is equal to 2 .2 .1 .2 centimeters, y is going to be equal to the sign of 19 .5 times a, which is going to be equal to 2 .12 times a sign of 19 .5.

04:39 That is 0 .71 centimeters...

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