You're visiting an aquarium that's the inverse of the...

You're visiting an aquarium that's the inverse of the situation in Example $31.4$ : Aquarium visitors occupy an air-filled cylindrical viewing room $6.00 \mathrm{~m}$ in diameter surrounded by the water of the aquarium, separated by a layer of strong glass that's thin enough for the refractive effect on light passing through the glass to be negligible. You're standing $1.25 \mathrm{~m}$ from the glass. A fish swims up to the glass and looks straight out at you. To the fish, how far away do you appear to be?

Key Concepts

Apparent Depth

The concept of apparent depth (or apparent distance) arises when an object observed across a boundary between two media, such as air and water, appears displaced from its actual position due to refraction. For rays near normal incidence, the apparent distance is typically scaled by the ratio of the refractive indices, causing objects to seem closer or farther than they really are. This principle is central when interpreting observations made across refractive interfaces.

Refraction

Refraction is the bending of light rays as they pass from one medium to another with a different refractive index. This bending occurs because the speed of light changes between media, causing the light ray to change direction at the interface. Understanding refraction is essential for determining how objects appear shifted from their true positions when viewed through different media.

Snell's Law

Snell’s Law is a fundamental principle that quantifies the relationship between the angles of incidence and refraction and the refractive indices of two media. It states that the product of the refractive index and the sine of the angle relative to the normal is constant across the interface. This law is pivotal in solving problems involving light transitioning between mediums and is used to compute apparent positions under refraction.

Transcript

00:01 So this is problem 3137, another variation of example 314 in the text.

00:08 I just drew a little sketch.

00:09 I'm at the top here where you're in an airfield cylindrical chamber inside of an aquarium.

00:17 So it's kind of the reverse of the example that's given in the text where it's a fish inside of a cylindrical aquarium.

00:24 So the person in this problem is 1 .25 meters from, oops, 1 .25 meters.

00:31 From the edge of the aquarium.

00:34 And we're looking at what the fish sees.

00:37 The problem asks, what a fish swims up to the glass and looks straight at you.

00:42 To the fish, how far away do you appear to be? so we're looking at finding the image distance when the person itself is the object.

00:52 So looking at it from a top view, they tell us that that person is 1 .25 meters from the edge.

00:59 So i'll write it here, but we're going to use it here.

01:03 This is our image, sorry, that's our object distance, 1 .25 meters, and i'll write it here, so it's a little clearer.

01:11 1 .25 meters.

01:13 And the diameter of that cylindrical air chamber is 6 meters, so the radius is 3 meters.

01:23 But the radius, the fish is looking, sorry, the object is on the, concave side.

01:30 The fish is the observer, but the object is on the concave side of that curve surface.

01:35 So we have to give that radius a negative sign.

01:39 So we have the radius of negative three.

01:41 The indices of refraction are water and air...

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