Exploring the Formation of Rainbows - Measuring Refractive Index

In summary, the diagram shows how a ray of light enters a raindrop and is reflected multiple times before exiting the drop. The ray is refracted according to the water's refractive index, which is about 1.3.
  • #1

Air

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Homework Statement


The diagrams below illustrate the formation of a rainbow. Figure 1 shows the general arrangement and Figure 2 shows the path of a ray through a raindrop with the centre of the raindrop is labelled O.

Figure 1:
Raindrop1.jpg


Figure 2:
Raindrop2.jpg


a.)
Where the ray enters the raindrop in Figure 2, mark the angle of incidence i and the angle of refraction, r.

b.)
Figure 2 is drawn to scale. By taking suitable measurements, show that the refractive index of water is about 1.3.


Homework Equations


[itex]\mu = \frac{\sin i}{\sin r}[/itex]


The Attempt at a Solution


a.)
Raindrop2Attempt.jpg

^ Have I labelled it correct?

b.)
I measured the angle that I have labelled above and got [itex]i = 25^\circ[/itex] and [itex]r = 35^\circ[/itex] and this gives [itex]\mu = 0.74[/itex]. This is incorrect. The correct answer is [itex]i = 53, \ r = 39, \ \implies \mu = 1.27[/itex]. Where have I gone wrong here?
 
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  • #2
The normal should be perpendicular to the water's surface.
 
  • #3
So, is it like this?

Raindrop2Attempt2.jpg
 
  • #4
Or, is it like this? :confused:

Raindrop2Attempt3.jpg
 
  • #5
You just seem to be drawing random lines lol...

The normal line on a spherical surface at some point P is always the line that goes from P through the center of the circle.

In other words; if you draw a straight line through the center of a circle, then at the points where it intersects the circle the angle between the line and the circle (at that point) is exactly 90 degrees, or perpendicular.
 
  • #6
Nick89 said:
You just seem to be drawing random lines lol...

The normal line on a spherical surface at some point P is always the line that goes from P through the center of the circle.

In other words; if you draw a straight line through the center of a circle, then at the points where it intersects the circle the angle between the line and the circle (at that point) is exactly 90 degrees, or perpendicular.

Oooh, I understand now. I guess it is this:

Raindrop2Attempt4.jpg


Am I correct?
 
Last edited:
  • #7
Yes, that looks good.
 

1. How do rainbows form?

Rainbows form when sunlight hits water droplets in the atmosphere and is refracted (bent) and reflected, separating the light into its component colors. The water droplets act like tiny prisms, causing the colors of the rainbow to appear.

2. What is refractive index?

Refractive index is a measure of how much a material can bend light. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material. The higher the refractive index, the more light is bent.

3. How do you measure the refractive index of a material?

The refractive index of a material can be measured using a device called a refractometer. This instrument uses the principle of Snell's Law to measure the angle at which light is bent as it passes through the material. The refractive index can then be calculated using this angle and the known refractive index of air.

4. Why is measuring the refractive index important?

Measuring the refractive index of a material is important for understanding how light interacts with the material. This information can be used in various fields such as optics, material science, and engineering. It can also help identify and distinguish different materials based on their refractive index values.

5. Can the refractive index of a material change?

Yes, the refractive index of a material can change depending on various factors such as temperature, pressure, and the wavelength of light passing through it. This is known as the material's dispersive properties. Additionally, different materials have different refractive indexes, so the refractive index can vary between different substances.

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