## Concept of Refractive Index

In this post, you will learn steps that will guide you on how to calculate an apparent displacement of a refractive index. But we first need to understand what the refractive index is.

**Definition:** Refractive index is a constant that is used to express the nature of the medium through which light ray is propagated. When a ray of light passes through a medium, the refractive index decides the length of it is permeability.

The symbol for the refractive index is μ and is constant

The formula for the refractive index is

μ = (Sin i) / (Sin r)

Also,

Refractive index (μ) = real depth / apparent depth

Therefore, we can now see that

Apparent depth = Real depth / Refractive index (μ)

Which is the formula for calculating apparent depth

The formula for calculating **apparent displacement (d) **is

d = t ( 1 – [1/μ] )

Where

d = apparent displacement

t = thickness

μ = refractive index

## Refractive Index: How to Calculate an Apparent Depth and Displacement

Here are a few examples that will help you understand how to calculate an apparent displacement

### Example 1

An ant is found under a regular glass slab of thickness 10.0cm and a refractive index of 1.7. Calculate the apparent displacement of the ant if viewed vertically from above the slab.

[UTME 2019]

Solution

To calculate the apparent displacement of the ant, we need to bring out the data from the question above

Data:

The thickness of the glass slab is the same as the Real depth ( t ) = 10.0cm

The refractive index of the glass slab is ( μ ) = 1.7

Now the last statement is telling us to calculate the apparent displacement ( d ) = ?

We can now use the formula below to calculate the apparent displacement

d = t ( 1 – [1/μ] )

Now we substitute the values of our data into the above equation

d = 10 ( 1 – [1/1.7] )

By dividing [1/1.7] inside the fraction we have 0.588

Now put [1/1.17] = 0.588 into the main d

d = 10 ( 1 – 0.588 )

Therefore

d = 10 x 0.412

which implies that our final answer is

d = 4.12cm

Therefore, the calculated apparent displacement of the ant vertically viewed from above the slab is 4.12cm

### Example 2

A microscope is focused on a table when a mark is covered by a plate of glass, 3cm thick. The microscope has to be placed 1.18 centimeters for the mark to be on a small focus. Calculate the refractive index of the medium.

**Solution:**

**Data**

Let us go through the question and pick our data

d = 1.18 cm

t = 3 cm

μ = ?

Now we need to apply the formula for apparent displacement

d = t ( 1 – [1/μ] )

Now we substitute our values from our data into the above formula

1.18 = 3 ( 1 – [1/μ] )

This is equal to

1.18 / 3 = ( 1 – [1/μ] )

Now we have

0.39 = 1 – [1/μ]

By taking 1 to the side of 0.39, we have

0.39 – 1 = – [1/μ]

Now we multiply each side by -1 to get

-1 ( 0.39 – 1) = – 1 ( – [1/μ] )

since multiplying negative by negative will give positive and negative by positive will give negative, we now have

1 – 0.39 = 1/μ

Simple arithmetic will give us

0.61 = 1/μ

By cross multiplication to make μ subject of the formula, we have

μ = 1/ 0.61 = 1.64

**You may also like to check**:

Resistivity Formula | Definition | Unit | Calculations

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