A glass sphere (n=1.50) with a radius of 15.0 cm has a tiny air bubble 5.00 cm above its center.

A glass sphere (n=1.50) with a radius of 15.0 cm has a tiny...

Key Concepts

Snell's Law

Snell’s law describes the relationship between the angles of incidence and refraction when a light ray passes from one medium into another with a different refractive index. It is fundamental in optics, stating that the product of the refractive index of the incident medium and the sine of the incident angle equals the product of the refractive index of the refracting medium and the sine of the refracted angle. This law is essential to understanding how light bends at interfaces, thereby contributing to phenomena such as the apparent displacement of immersed objects.

Apparent Depth

The concept of apparent depth refers to the phenomenon where objects submerged in a medium appear closer to the surface than they truly are, due to the bending of light rays at the interface between media of different refractive indices. This effect arises because light travels at different speeds in different media, causing the refracted rays to mislead the observer about the true position of the object. This principle is widely applicable in optical problems involving water or glass, where it is necessary to relate the real depth of an object to its perceived depth.

Refraction at a Curved Interface

Refraction at a curved interface pertains to how light behaves when passing through a boundary that is not flat, such as a spherical surface. Unlike planar interfaces, the curvature means that the normal to the surface – and hence the angle of incidence – varies at different points. Understanding this concept is important for analyzing optical systems like lenses and spherical containers, as it influences the overall path of refracted rays and the resulting image position and distortion.

Transcript

00:02 So here we have a spherical glass with a piece of an object that's inside of this glass.

00:13 And we want to find, based on the position that this object is from the center of this spherical glass, what is the apparent depth that someone sees this object when viewed from above.

00:29 So from the top view, you have an object that's located at the center.

00:33 Of this spherical glass here.

00:37 And from the side view, you can see that there's the center point here, and the object is located above that center point.

00:48 It's displaced 5 centimeters above the center.

00:52 So from the surface, it's actually 10 centimeters, and the radius of the spherical glass is 15 centimeters.

01:00 So what we want to do is we want to be able to use the equation for refractive surfaces, for cyrical refractive surfaces to find the image of this object that we have here.

01:18 What we're given, we're given the index of refraction for glass.

01:29 That is 1 .5.

01:39 And from this, we can see what our, we can, we'll redraw this to see what our object distance is.

01:49 Our object distance is going to be 10 centimeters because our object distance is measured from the object to the refractive surface.

02:01 And the refractive surface is going to be this edge here.

02:12 And if you can imagine someone looking down at this refractive surface, they're going to be looking at from this angle.

02:19 So the object is displaced 10 centimeters from the surface.

02:27 So the object length is 10 centimeters.

02:31 Now, the radius of, so let's redraw this so that we can make this a little bit clear.

02:54 So we said that this is going to be 15 centimeters.

02:58 I'm sorry, 10 centimeters.

03:01 The difference between the object and the refractive surface.

03:09 And also, we have a radius of course.

03:13 Curvature for this refractive surface.

03:16 And for a refractive surface that is curved this way, that's curved sort of a concave, we measure the radius to be negative.

03:31 So the radius is actually negative 15 centimeters...

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