A transparent rod 30.0 cm long is cut flat at one end and...

A transparent rod 30.0 $\mathrm{cm}$ long is cut flat at one end and rounded to a hemispherical surface of radius 10.0 $\mathrm{cm}$ at the other end. A small object is embedded within the rod along its axis and halfway between its ends, 15.0 $\mathrm{cm}$ from the flat end and 15.0 $\mathrm{cm}$ from the vertex of the curved end. When viewed from the flat end of the rod, the apparent depth of the object is 9.50 $\mathrm{cm}$ from the flat end. What is its apparent depth when viewed from the curved end?

A transparent rod 30.0 $\mathrm{cm}$ long is cut flat at one end and rounded to a hemispherical surface of radius 10.0 $\mathrm{cm}$ at the other end. A small object is embedded within the rod along its axis and halfway between its ends, 15.0 $\mathrm{cm}$ from the flat end and 15.0 $\mathrm{cm}$
from the vertex of the curved end. When viewed from the flat end of the rod, the apparent depth of the object is 9.50 $\mathrm{cm}$ from the flat end. What is its apparent depth when viewed from the curved end?

Key Concepts

Refraction

Refraction is the phenomenon in which light bends as it passes from one medium to another due to a change in its speed. This change in direction occurs at the interface of materials with differing refractive indices and is foundational to understanding how optical devices and phenomena, such as the apparent shift in position of an object within a transparent medium, work.

Apparent Depth

Apparent depth refers to the perceived position of an object observed through a refractive medium. Due to the bending of light at the boundary between different media, the object appears closer to the surface than it actually is. This concept is often quantified by comparing the actual depth to the apparent depth using the refractive index of the medium.

Refractive Index

The refractive index is a measure of how much the speed of light is reduced inside a medium compared to its speed in vacuum. It is a critical parameter in optics because it influences the degree of light bending during refraction. The refractive index directly affects how an object’s depth is perceived when viewed through a medium.

Snell's Law

Snell's Law governs the relationship between the angles of incidence and refraction when light passes between two media with different refractive indices. Expressed as n? sin(??) = n? sin(??), this principle is essential for calculating the bending of light, which in turn affects phenomena such as apparent depth and the formation of virtual images.

Virtual Image Formation

Virtual image formation occurs when light rays passing through a medium appear to diverge from a location where no actual light is coming from. This concept explains how objects can appear to be at different positions from where they truly are, particularly when viewed through interfaces between media with different refractive indices.

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