Understanding True vs Apparent Depth

The difference between true depth and apparent depth lies in the way light behaves when it passes from one medium to another, such as from air to water. True depth refers to the actual distance between the observer and the object underwater, while apparent depth is the perceived distance of the object as seen by an observer above the water’s surface.

When light travels from one medium to another, such as from air to water, it changes speed and direction due to the difference in optical density between the two mediums. This change in speed and direction causes the light rays to bend or refract. As a result, objects underwater appear to be at a different position than their actual location, which creates the illusion of a different depth. This phenomenon is what causes a straw in a glass of water to appear bent.

The relationship between true depth and apparent depth can be described by the formula:

$\frac{1}{\text{apparent depth}} = \frac{n_2}{n_1} \times \frac{1}{\text{true depth}}$

where $n_1$ is the refractive index of the medium from which the light is coming (e.g., air), and $n_2$ is the refractive index of the medium through which the light is passing (e.g., water).

The concept of true depth and apparent depth is fundamental in understanding how light behaves when it travels through different mediums. This phenomenon, known as refraction, occurs because light changes speed when it moves from one medium to another. The speed of light is different in air compared to water or glass, for example, due to the differing densities of these materials.

When light passes from a less dense medium (like air) to a denser one (like water), it slows down and bends towards the normal line (an imaginary line perpendicular to the surface separating the two mediums). This bending causes objects to appear higher or shallower than they actually are, which is why a swimming pool often looks shallower than it really is.

The amount of bending depends on the refractive indices of the two mediums. The refractive index is a measure of how much light slows down in a particular medium compared to its speed in a vacuum. For example, the refractive index of air is approximately 1.0003, while the refractive index of water is about 1.333. This means that light travels about 1.333 times slower in water than in a vacuum.

The relationship between true depth, apparent depth, and refractive indices can be further explored through the lens of Snell’s Law, which describes the bending of light at the interface between two mediums:

$n_1 \times \sin(\theta_1) = n_2 \times \sin(\theta_2)$

where:

• $n_1$ and $n_2$ are the refractive indices of the two mediums,
• $\theta_1$ is the angle of incidence (the angle between the incident ray and the normal), and
• $\theta_2$ is the angle of refraction (the angle between the refracted ray and the normal).

This law quantifies how much light bends at the interface, which in turn affects the apparent depth of objects in a different medium.

Understanding the difference between true depth and apparent depth is not only important for optical phenomena like mirages and the appearance of objects in water but also has practical applications in fields such as optics, underwater photography, and even the design of corrective lenses for vision correction.