How to Calculate the Refractive Index in Physics

Reviewed by Joseph Meyer

Last Updated: November 14, 2023 Fact Checked

When light passes through a surface, the straight beam of light is bent. The beam travels through the object along a different path than the beam was following when it entered the object. The beam of light bends again when it leaves the object. These bends at the surface boundaries between air and the object are called refraction. Refraction is caused by the fact that light travels at a constant speed only in a vacuum. When light passes through another object, the light is slowed down. The bend caused by this slowing can be calculated based on the refractive index of the object. The refractive index of an object is the ratio of the speed of light in a vacuum to the speed of light in the object.^{[1]
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Research source} Use these tips to learn how to calculate the refractive index in physics.

Method 1

Method 1 of 2:

Determine the Measurements Needed For the Calculation

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For example, a pane of window glass has a thickness that may be stated by the manufacturer, but which should be measured to ensure accurate calculation of the refractive index.
Monochromatic point light sources are available through laboratory supply outlets. Place the point light source a known distance from the surface of the object. Aim the point light source into the object perpendicularly to the point on the object being struck. Mark the other side of the object at the point where the light emerges.^{[2]
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Move the light source such that a line drawn between the perpendicular placing of the light source and the angled placing of the light source forms a right angle. Note the point where the light emerges on the other side of the object. Mark that point where the light emerges.^{[3]
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Method 2

Method 2 of 2:

Calculate the Angle Of Refraction

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The first leg will be the distance that the point light source was placed from the object to make the perpendicular. The second leg will be the lateral distance that the point light source was moved from the perpendicular generation point to the angled generation point. The third leg, the hypotenuse, can be determined as the square root of the sum of the squares of the other 2 sides.
The first leg will be the thickness of the object. The second leg will be the distance between the 2 marks on the back of the object. The third leg, the hypotenuse, is defined as the square root of the sum of the squares of the other 2 sides.
Knowing the dimensions of the triangles, the angles at the boundary between the air and the surface of the object can be calculated using trigonometry. The angle on the air side of the interface is the angle of incidence. The angle on the object side of the interface is the angle of refraction.^{[4]
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$Step 4 Calculate the refractive index.$

The refractive index of the object is the sine of the angle of incidence divided by the sine of the angle of refraction.^{[5]
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Why do I need to read physics?

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Physics is an important concept in life, and learning physics can explain the causes of phenomenons that are happening around you all the time. Also, the history of important scientists in physics can be both inspiring and informative.

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I'm not sure about the angle in air, I always thought it was the angle alternate to the one indicated here. Is this accurate?

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Generally, we consider the angle made by the refracted ray with the normal. The angle shown here is equal to it, so it's accurate.

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How do I make a virtual image refraction math problems for physics?

Sarthik Garg

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We need to place the object at distance less than focus for a concave mirror and convex lens; convex mirror and concave lens always gives virtual image.

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