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$\bullet$$\bullet$ A thin beam of light in air is incident on the surface of a lanthanum flint glass plate having a refractive index of 1.80 . What is the angle of incidence, $\theta_{a}$ of the beam with this plate, for which the angle of refraction is $\theta_{a} / 2 ?$ Both angles are measured relative to the normal.

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$51.7^{\circ}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 23

Electromagnetic Waves and Propagationof Light

Electromagnetic Waves

Reflection and Refraction of Light

Rutgers, The State University of New Jersey

Hope College

University of Sheffield

University of Winnipeg

Lectures

02:30

In optics, ray optics is a geometric optics method that uses ray tracing to model the propagation of light through an optical system. As in all geometric optics methods, the ray optics model assumes that light travels in straight lines and that the index of refraction of the optical material remains constant throughout the system.

10:00

In optics, reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Reflection may also be referred to as "mirror image" or "specular reflection". Refraction is the change in direction of a wave due to a change in its speed. The refractive index of a material is a measure of its ability to change the direction of a wave. A material with a higher refractive index will change the direction of a wave to a greater degree than a material with a lower refractive index. When a wave crosses the boundary between two materials with different refractive indices, part of the wave is refracted; that is, it changes direction. The ratio of the speeds of propagation of the two waves determines the angle of refraction, which is the angle between the direction of the incident and the refractive rays.

02:49

A narrow beam of light is …

03:43

A parallel beam of light m…

04:16

01:36

A beam of light in air is …

01:09

A beam of light is inciden…

01:56

0:00

A beam of light in air ent…

03:24

$\bullet$ A beam of light …

08:52

Light moves from flint gla…

01:03

A light ray is incident fr…

01:16

A light beam in air has an…

02:08

$\bullet$$\bullet$ A beam …

01:24

A beam of unpolarized ligh…

In this problem, we are going to calculate the angle of incidence for which the angle of reflection becomes itself, so we call the angle of incidence as theta. In order to calculate this angle, let me apply the snath lies n, a sine theta equals to n g sine theta a by 2. Let'S call it equation number 1 here this na is the reflection of the air, and the n g is the reflection of the material. Now we can write the sine theta a is a sine theta equals to sine 2 into theta a divided by 2, and this relation is equals to 2 sine theta, a divided by 2 cosine theta a divided by 2. Now, in setting this value into equation number 1, we can write, it is n a and then there is 2 sine theta, a divided by 2 cosine theta, a divided by 2 equals to n g sine theta a divided by 2. From here we can write cosine theta, a by 2 equals to n g divided by 2 n a and it can be written for thet. I is theta equals to 2 ar cosine o n g divided by 2 and a we call this equation as equation. Number 1 now be in setting the values into this equation. We can write theta equals to 2 arcosineof. His ng is equals to 1.80 divided by 2 into 1.00, so this will go as the value for theta is theta equals to 51.7 degrees. So this is the required answer. Thank you.

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