Light of wavelength 700 nm is incident on the face of a fused quartz prism (n=1.458 at 700 nm)

Light of wavelength 700 nm is incident on the face of a...

Light of wavelength 700 $\mathrm{nm}$ is incident on the face of a fused quartz prism $(n=1.458 \text { at } 700 \mathrm{nm})$ at an incidence angle of $75.0^{\circ} .$ The apex angle of the prism is $60.0^{\circ} .$ Calculate the angle (a) of refraction at the first surface, (b) of incidence at the second surface, (c) of refraction at the second surface, and (d) between the incident and emerging rays.

Key Concepts

Deviation of Light through a Prism

The deviation of light through a prism is the total angular change in the light path between the incident ray and the emerging ray. This concept combines the effects of refraction at both surfaces of the prism and depends on the prism’s geometry and the index of refraction of the material. Computing the deviation involves using Snell's Law at each interface and applying geometric relationships to find the final angle between the incident and emergent rays.

Snell's Law

Snell's Law explains how light bends (refracts) at the boundary between two media with different optical densities. It quantitatively relates the sine of the angle of incidence to the sine of the angle of refraction, proportional to the indices of refraction of the two media. This law is fundamental in determining how a light ray changes direction as it enters or exits a prism.

Index of Refraction

The index of refraction is a measure of how much the speed of light is reduced in a given medium compared to its speed in vacuum. It plays a crucial role in determining the degree of bending of light as it crosses an interface between two materials. In problems involving refraction through a prism, the index allows for the calculation of angles of incidence, refraction, and ultimately the overall deviation of the light ray.

Prism Geometry

Prism geometry refers to the specific angular relationships inside a prism, including the apex angle, which is the angle between the two refracting surfaces. The geometry of the prism is essential for understanding the internal path of light rays as they undergo successive refractions. Correctly relating the angles at the prism surfaces allows one to compute the light’s trajectory within the prism.

Transcript

00:01 Called that we have a prism with an apex angle of 60 degrees, right? and it has an angle of incidence of 75 degrees.

00:09 So we want to find out first what theta 2 is.

00:12 That's the angle of emergence inside the prism, or refraction rather.

00:19 So that's the angle of refraction.

00:21 So the equation that we use for this is n1, sine of 1, of theta 1.

00:30 Is equal to n2, sine of theta 2.

00:33 So n1 is equal to 1 because that's in the air.

00:36 And n2, which is the quartz prism, is 1 .458.

00:43 And you can find this in the table in your book.

00:46 So sign of theta, so in order to find theta 2, we're going to have to set this equal to, we're going to have to find the inverse sign of sine, of theta 1 over n2.

01:05 So this is going to be equal to the inverse sign of sine of 75 because that is theta 1 over 1 .458.

01:21 So that means our theta 2 is going to be equal to 41 .5 degrees.

01:36 Excellent.

01:38 So next thing we're going to do is we're going to find out what angle, what theta 3 is.

01:45 So we want to first find out what this angle is.

01:49 So this angle, since this is making, this is normal, right? this is perpendicular to this line.

01:55 That means that this plus this is going to be equal to 90.

01:58 So if theta 2 plus, we'll call this x, is equal to 90, and that means that x is equal to 90 minus 41 .5, which means that x is equal to, 48 .5...

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