What is the Approximate Index of Refraction of a Transparent Liquid?

In summary, the problem involves finding the index of refraction of a transparent liquid by using Snell's law. The image of a small object floating at the surface of the liquid is seen at 14 cm below the surface, which is used to calculate the approximate value of the index of refraction. The solution involves using the Pythagorean theorem and assuming small angles to simplify the calculations. The problem allows for an approximate answer due to the dependency of the index of refraction on the distance x, which is a small value.
  • #1
Perrin
14
0

Homework Statement



The original problem:

A plane mirror is placed horizontally at the bottom of a transparent liquid of 10 cm depth. When one looks at the image of a small object floating at the surface of the liquid right above the object, the image is seen at 14 cm below the surface of the liquid. Find the approximate value of the index of refraction of the liquid.

Homework Equations



I used Snell's formula:
sin(alpha1)/sin(alpha2) = n2/n1

The Attempt at a Solution



http://www.dotcore.co.il/refraction_problem.jpg [Broken]
I really hope this image is clear enough, unfortunately that's the top of my Gimp skills...

I said:
sin(alpha1)/sin(alpha2) = n2 (n1 = 1 because it's the index of refraction of air)

sin(alpha1) = BF/AF, sin(alpha2)=DC/AC
DC=FB=x, because the image as seen by the observer as result of the refraction is right above the original image
So:
n2 = (x/AF)/(x/AD) = AD/AF

According to the Pythagorean theorem:
AD = sqrt(x^2 + 20^2)
AF = sqrt(x^2 + 14^2)

Now to my problem:
Certainly, n2 depends on x. I remember my textbook saying that a point below the surface of a material with a higher index of refraction does not create a clear image, is that the reason of the dependency of n2 on x?
The book also said that for small distances, the image can be seen clearly. Does that mean that I can plug in a small value for x to get the correct answer? I tried plugging in x=0, and I got a correct answer. Is it valid to do that? Is that the reason the problem states "Find the approximate value"?

Thanks in advance for the help!
Perrin.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Pretty much that looks like it.

For a small angle I think you can reasonably take AF ≈ AB and AC ≈ AD.
 
  • #3
OK, thanks for affirming my answer! I can sleep peacefully tonight :D
 

1. What is refraction in optics?

Refraction in optics is the bending of light as it passes through a medium with a different density. This causes the light's path to change direction as it enters and exits the medium, resulting in a change in the speed and wavelength of the light.

2. How does refraction affect the shape of objects?

Refraction can cause objects to appear distorted or shifted when viewed through different mediums. This is due to the change in the path of light as it passes through the mediums, causing a change in the angle of incidence and the apparent position of the object.

3. What is Snell's law and how is it related to refraction?

Snell's law is a principle that describes the relationship between the angle of incidence and the angle of refraction when light passes through two different mediums. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two mediums.

4. How does refraction impact the design of optical instruments?

Refraction is a key factor in the design of optical instruments such as lenses and prisms. These instruments use the principles of refraction to manipulate and focus light, allowing for the formation of clear images and magnification.

5. What factors can affect the degree of refraction in a medium?

The degree of refraction in a medium can be affected by several factors, including the density and composition of the medium, the angle of incidence of the light, and the wavelength of the light. Temperature and pressure can also impact the degree of refraction in some mediums.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
882
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
24
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
Replies
11
Views
295
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Back
Top