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

step 1 By finding image location of the bubble, of a bubble, we can find a pattern depth. So using the

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

A glass sphere $(n=1.50)$ with a radius of 15.0 $\mathrm{cm}$ has a tiny air bubble 5.00 cm above its center. The sphere is viewed looking down along the extended radius containing the bubble. What is the apparent depth of the bubble below the surface of the sphere?

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.

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