As is drawn in Fig. 37-4, a ray of light in air strikes a...

As is drawn in Fig. $37-4$, a ray of light in air strikes a glass plate $(n=1.50)$ at an incidence angle of $50^{\circ}$. Determine the angles of the reflected and transmitted rays. The law of reflection applies to the reflected ray. Therefore, the angle of reflection is $50^{\circ}$, as shown. For the refracted ray, $n_{i} \sin \theta_{i}=n_{t} \sin \theta_{t}$ becomes $$ \sin \theta_{t}=\frac{n_{i}}{n_{t}} \sin \theta_{i}=\frac{1.0}{1.5} \sin 50^{\circ}=0.51 $$ from which it follows that $\theta_{t}=31^{\circ}$.

As is drawn in Fig. $37-4$, a ray of light in air strikes a glass plate $(n=1.50)$ at an incidence angle of $50^{\circ}$. Determine the angles of the reflected and transmitted rays.
The law of reflection applies to the reflected ray. Therefore, the angle of reflection is $50^{\circ}$, as shown.
For the refracted ray, $n_{i} \sin \theta_{i}=n_{t} \sin \theta_{t}$ becomes
$$
\sin \theta_{t}=\frac{n_{i}}{n_{t}} \sin \theta_{i}=\frac{1.0}{1.5} \sin 50^{\circ}=0.51
$$
from which it follows that $\theta_{t}=31^{\circ}$.

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Key Concepts

Index_of_Refraction

The index of refraction is a property of a medium that describes how much the speed of light is reduced within that medium compared to its speed in a vacuum. It is a crucial parameter in understanding both refraction and the behavior of light as it transitions between different materials, as seen in Snell's Law.

Snells_Law

Snell's Law relates the angles of incidence and refraction when light passes from one medium to another with different optical densities. It is expressed as n_i sin(?_i) = n_t sin(?_t), where n_i and n_t represent the indices of refraction of the initial and transmitting media, respectively. This law explains how the change in speed of light between media leads to bending, or refraction, of the light ray.

Law_of_Reflection

The law of reflection states that when a light ray strikes a smooth surface, the angle at which it approaches the surface (angle of incidence) is equal to the angle at which it leaves the surface (angle of reflection). This concept is fundamental in optics and applies to all reflecting surfaces, ensuring that the incident and reflected rays are symmetrical with respect to the normal at the point of contact.

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