Apparent Depth Formula
D(Apparent) = D(Real) / μ21
Where,
- D(apparent) is the apparent depth of an object,
- D(real) is the real depth of an object, and
- μ21 is the relative refractive index of medium 2 with respect to medium 1 and is given as:
μ21 = μ2 / μ1
Derivation of Apparent Depth Formula
To derive the formula for apparent depth we will follow the figure given below:
A light ray originating from the coin gets refracted and moves away from the normal. When it is traced back, we can determine the position of the virtual object. To determine the position of the virtual object, at least two rays of light are needed. In this diagram, the primary purpose is to illustrate the concept of apparent depth.
We can perform below calculations referring the figure.
cos(90−θ1) = sin(θ1) = X / D(apparent) —–(1)
and cos(90−θ2) = sin(θ2) = X / D(real) —–(2)
Dividing (1) and (2) ,
sin(θ1) / sin(θ2) = D(apparent) / D(real)
Using Snell’s Law
μ12 = 1/μ21 = μ1/μ2 = sin(θ1)/sin(θ2)
⇒ D(apparent) / D(real) = 1/μ21
⇒ D(apparent) = D(real) /μ21
Which is the required formula.
Apparent Depth
Apparent Depth is an example of reflection of light from different mediums and can be observed in many areas. Such as when we drink water from a bottle or any vessel we have an illusion that the bottle’s base is very near to us, but after it gets empty we realize its actual depth. This illusion is a result of the phenomenon known as Apparent Depth. Apparent Depth plays a crucial role in our perception of objects submerged in liquids as there are many such examples like a fish in a pond appearing near to the surface, the bottom of the Swimming Pool appearing near to the surface, and many more.
In this article, we will dive deep into the phenomenon of apparent depth, exploring its definition, the laws of refraction governing it, its mathematical formulation, the factors affecting it, and solving a problem to solidify our understanding.
Table of Content
- What is Apparent Depth?
- Apparent Depth in Different Medium
- Apparent Depth Formula
- Apparent and Real Depth
- Factors Affecting Apparent Depth