The light ray shown in the figure below makes an angle of 20.0^∘ with the normal line at the bou

The light ray shown in the figure below makes an angle of...

Key Concepts

Index of Refraction

A property of a material that quantifies how much the speed of light is reduced inside the material compared to its speed in a vacuum. It plays a crucial role in determining the degree of bending, or refraction, of light as it transitions between different media.

Angle of Incidence and Angle of Refraction

These are the angles formed between the incoming or refracted light ray and the normal—an imaginary line perpendicular to the surface at the point of incidence. The relationship between these angles, governed by Snell's Law, is fundamental for understanding and calculating the change in the direction of light when it passes between media.

Snell’s Law

An essential principle in optics stating that the product of the index of refraction and the sine of the angle (measured from the normal) remains constant as light passes from one medium to another. This law, expressed as n1 sin(theta1) = n2 sin(theta2), is used to determine how much a light ray bends when entering a medium with a different refractive index.

Transcript

00:01 Alrighty.

00:02 So to solve this problem, what we're going to do is we're going to split it up into two sections.

00:06 We're going to start with the air oil section that the light goes through, and we're going to calculate theta 1 using snell's law.

00:14 And then we're going to move on to the oil water section that the light ray goes through, and we're going to calculate theta 2 by using snell's law again.

00:23 All right, so let's begin.

00:24 We're going to begin with the air oil section.

00:32 Okay.

00:34 So we're going to use snell's law.

00:35 So i'm going to take the...

00:36 Index of refraction of air multiply it by the sign of theta 1 and then we're going to set that equal to the index of refraction of oil multiplied by the sign of the given angle which is actually 20 degrees and what we're going to do is we're going to take this equation and we're going to use it to solve for what this angle is right here all right so now let's plug in our givens and then rearrange the equation to get theta 1 by itself so the index every fraction of air is actually just one.

01:19 So we're not even going to write it down.

01:21 So i'm just going to start by writing down sign theta 1.

01:26 We don't know what data 1 is yet, so i'm just going to leave it as data 1 for now.

01:31 We're given that the index every fraction of linseed oil, which is the oil for this section, is 1 .48.

01:40 They do this by going into a lab and doing experiments and figuring out what the index every fraction of the oil is.

01:47 And then you take that 1 .48 and then multiply it by the sign of 20 degrees.

01:53 Okay, so remember that 1 .48 is one number and sign of 20 degrees is another number.

02:01 All right, so what we need to do is we need to get this to say theta 1 equals some number.

02:08 The issue we're having is that we have this sign attached to the theta 1.

02:13 So we're not going to just divide sign on both sides.

02:18 Like you do in algebra where you divide a number.

02:21 What you need to do is you need to take the inverse sign of both sides.

02:25 So you're going to have to use that inverse sign button in your calculator.

02:30 So theta 1 is going to be equal to the inverse sign of 1 .48 multiplied by the sign of 20 degrees.

02:46 You can plug all of this into a calculator.

02:51 All right.

02:52 So if you do this correctly, you'll get that theta 1, is equal to 30 .4 degrees.

03:02 Make sure that calculator is in degrees and it is not in radiance.

03:07 All right.

03:08 So now we know what theta one is...

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