In Fig. 33-48 a, a light ray in water is incident at angle θ1 on a boundary with an underlying m

step 1 For this problem on the topic of electromagnetic waves, we are shown in the figure a light ray i

In Fig. 33-48 a, a light ray in water is incident at angle...

In Fig. $33-48 a,$ a light ray in water is incident at angle $\theta_{1}$ on a boundary with an underlying material, into which some of the light refracts. There are two choices of underlying material. For each, the angle of refraction $\theta_{2}$ versus the incident angle $\theta_{1}$ is given in Fig. $33-48 b$. The vertical axis scale is set by $\theta_{2 x}=90^{\circ}$. Without calculation, determine whether the index of refraction of (a) material 1 and (b) material 2 is greater or less than the index of water $(n=1.33) .$ What is the index of refraction of (c) material 1 and (d) material $2 ?$

In Fig. $33-48 a,$ a light ray in water is incident at angle $\theta_{1}$ on a boundary with an underlying material, into which some of the light refracts. There are two choices of underlying material. For each, the angle of refraction $\theta_{2}$ versus the incident angle $\theta_{1}$ is given in Fig. $33-48 b$. The vertical axis scale is set by $\theta_{2 x}=90^{\circ}$. Without calculation, determine whether the index of refraction of
(a) material 1 and (b) material 2 is greater or less than the index of water $(n=1.33) .$ What is the index of refraction of (c) material 1 and (d) material $2 ?$

Key Concepts

Snell’s Law

Snell’s Law relates the angles of incidence and refraction for a light ray crossing an interface between two media with different indices of refraction. It is mathematically expressed as n? sin(??) = n? sin(??), where n? and n? are the indices of refraction of the first and second media respectively, and ?? and ?? are the angles measured from the normal. This law is fundamental in understanding how light bends when entering a different medium.

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 central to predicting the behavior of light as it passes from one medium to another because differences in indices cause the light ray to change direction. A higher index indicates that light travels more slowly in that medium compared to one with a lower index.

Critical Angle

The critical angle is the angle of incidence in a denser medium at which the refracted ray in the less dense medium would travel along the interface (i.e., at 90° to the normal). It is derived by setting the refraction angle to 90° in Snell’s Law. This concept is crucial for understanding phenomena such as total internal reflection, which occurs when the angle of incidence exceeds the critical angle, preventing the light from passing into the second medium.

Refraction at a Boundary

Refraction at a boundary refers to the bending of a light ray as it passes from one medium into another, governed by the change in its speed resulting from the differing optical densities of the media. The extent of bending is determined by the indices of refraction of the two media, and this concept is essential for analyzing and predicting the behavior of light in various optical systems.

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