(II) An aquarium filled with water has flat glass sides...

(II) An aquarium filled with water has flat glass sides whose index of refraction is $1.52 .$ A beam of light from outside the aquarium strikes the glass at a $43.5^{\circ}$ angle to the perpendicular (Fig. $23-49 ) .$ What is the angle of this light ray when it enters $(a)$ the glass, and then $(b)$ the water? (c) What would be the refracted angle if the ray entered the water directly?

Key Concepts

Snell's Law

Snell's Law, commonly expressed as n? sin?? = n? sin??, is the fundamental law governing the refraction of light between two media with different indices of refraction. It explains how the angle of incidence relates to the angle of refraction when light passes from one medium to another, and is critical for calculating how light rays bend at interfaces.

Index of Refraction

The index of refraction is a measure of how much the speed of light is reduced in a medium compared to its speed in a vacuum. It determines the degree of bending or slowing of light as it enters a new medium. Differences in the refractive indices of materials like air, glass, and water directly affect the path of light according to Snell's Law.

Angle of Incidence and Refraction

The angle of incidence is the angle between the incoming light ray and the normal (perpendicular) to the surface, while the angle of refraction is the angle between the refracted ray and the normal in the new medium. These angles are linked through Snell's Law, and understanding them is essential for predicting and calculating the path of light as it crosses an interface.

Refraction at Multiple Interfaces

When light passes through multiple media (for example, from air into glass and then into water), each interface leads to a partial refraction determined by the respective indices of refraction. It is important to apply Snell's Law at each boundary separately to accurately determine the final direction of the light ray.

Transcript

00:01 Okay, in this problem, we have an aquarium and it's filled with water and it has a glass sides and their index of refraction is 1 .52.

00:12 So let's write that first given down.

00:16 That ng is equal to 1 .52.

00:24 Let's go ahead and look at the figure while we're at it and i'll pause the video while i pull it up.

00:30 Okay, got it.

00:32 So we have glass and then we have water and we have light entering.

00:45 And this angle is i think 43 .5 degrees.

00:50 Let's double check.

00:52 Yeah, great.

00:54 And we want to get the angle of the ray when it enters the glass and then the water.

01:04 So first let's write down the index of a fraction of.

01:07 Of water.

01:09 So that's nw and that value is 1 .33.

01:18 So let's find what the angle is when it goes into the glass.

01:23 So here's the glass and here's the water.

01:27 So for that we want to use snell's law so we can say ng sine theta, g is equal to an air sign of theta in the air.

01:42 And then this is, of course, one.

01:45 So if we want to solve for theta g, we want to divide both sides by ng and then take the arc sign of both sides.

01:52 So with that, we can say theta g is equal to the arc or the inverse sign of n .a., which is 1 over ng, multiplied by the sign of the angle and the air.

02:07 And that theta error is 43 .5.

02:13 So i'll go ahead and write that out explicitly.

02:16 Great.

02:16 So now we have a formula and we have everything we're looking for in the formula.

02:20 So i just need to plug it into a calculator.

02:23 So i'm going to do arc sign of 1 over 1 .52 times the sign of 43 .5 degrees.

02:35 And convert that to degrees.

02:40 So that is 26 .9 degrees.

02:48 And then we also want the angle in water...