A beam of light in air enters a glass block at an angle of 30^∘ to the glass surface, as shown.

A beam of light in air enters a glass block at an angle of...

A beam of light in air enters a glass block at an angle of $30^{\circ}$ to the glass surface, as shown. The glass has an index of refraction of $1.35 .$ (a) Find the angle labeled $\theta_{1}$. (b) Calculate the critical angle between the glass and air. (c) Does the light follow path $A$, path $B$, or both? Explain. (d) Find the angle(s) $\theta_{A}$, if light follows path $A,$ and $\theta_{B},$ if light follows path $B$

Key Concepts

Snell's Law

Snell's law mathematically describes the relationship between the angles of incidence and refraction when light passes between two media. It is expressed as n? sin(??) = n? sin(??), where n? and n? are the refractive indices of the respective media, and ?? and ?? are the angles with respect to the normal.

Total Internal Reflection

Total internal reflection is the phenomenon where all the light is reflected back into the denser medium and none is refracted into the less dense medium. This occurs when the angle of incidence exceeds the critical angle, ensuring that the light remains confined within the original medium.

Refraction

Refraction is the bending of a light ray as it passes from one medium into another with a different optical density. This change in direction occurs because the speed of light differs in the two media, and it is governed by the angle of incidence and the refractive indexes of the media involved.

Refractive Index

The refractive index is a measure of how much light slows down in a given medium compared to its speed in a vacuum. It is a fundamental property of a medium that determines how much the light bends when entering or leaving it, and it is used in calculations such as Snell's law.

Critical Angle

The critical angle is the minimum angle of incidence in the denser medium at which total internal reflection occurs, meaning that the refracted ray travels along the boundary. It is calculated using the indices of refraction of the two media, typically by setting the angle of refraction to 90° in Snell's law.

Transcript

00:01 For this problem, we want to consider light incident on a glass block as shown in the figure.

00:09 For part a, we want to find theta 1.

00:13 For part b, we want to find the critical angle.

00:17 For part c, we want to determine if light travels along path a or b.

00:24 And for part d, we want to figure out the angle corresponding to the path, the light travels along.

00:33 So for part a, in order to find theta 1, it's going to be easier to find the angle of refraction and then subtract that from 90 degrees to get theta 1.

00:47 It turns out that the angle of incidence should be 60 degrees because it makes a 90 degree angle when added to the 30 degree angle we already know.

00:59 And so we can use that information and snell's law to find theta 1.

01:05 We would have that the index of refraction of air times the sign of 60 degrees should equal the index of refraction of the glass times sign of what i'm going to call theta.

01:19 And again, theta 1 will be 90 minus theta.

01:24 We can solve this for theta and get that theta is 39 .9.

01:32 038 degrees.

01:35 And so theta 1, which is 90 minus theta, is equal to 50 .0962 degrees, or about 50 .1 degrees.

01:50 For part b, we need to find the critical angle.

01:54 The critical angle theta c is always found by taking the inverse sign of the transmissible...

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