Using snell's law, observations thru a glass of water & glass of air

In summary, the observer in the figure is trying to calculate the height of a glass filled with water, based on its width and the position of its center of the bottom. After using Snell's law and solving for h, the calculated height is 2.366 cm, which may seem unreasonable but is in fact correct.
  • #1
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Homework Statement



The observer in the figure shown below is positioned so thatthe far edge of the empty glass is just visible. When theglass is filled with water, the center of the bottom of the glassis just visible to the observer. Calculate the height H of theglass if its width W=4 cm.

20086101213226334869680211712505078.jpg


Homework Equations


snell's law


The Attempt at a Solution



sin theta = 2r/root(4r^2 + h^2) -AIR
sin phi = r/ root(r^2+h^2) -WATER

plug into snell's law:

n1sintheta = n2sinphi

(1) 2r/root(4r^2 + h^2) = (1.333) r/ root(r^2+h^2)

And then from there I solve for h. . . i cross multiply to eliminate the denominators and then square both sides to get rid of the square root signs.

So then. .

h^2 = 5.6 cm
h= 2.366 cm.

Please help! I don't know what I'm doing wrong, but the answer doesn't seem reasonable at all. :( It's totally insane. . .
 
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  • #2
hi imatreyu! :smile:

(have a square-root: √ and try using the X2 icon just above the Reply box :wink:)

that's a bit long-winded, but i get the same answer, 2√(7/5) :wink:
 
  • #3
Your answer is correct.
 

1. How does Snell's law explain the bending of light when observed through a glass of water and a glass of air?

Snell's law is a principle in physics that describes how light bends when it travels from one medium to another. In the case of observing light through a glass of water and a glass of air, the light is traveling from air (a less dense medium) to water (a more dense medium). Snell's law states that the angle of incidence (the angle at which the light enters the medium) is directly proportional to the index of refraction of the medium. This means that as light enters a more dense medium, it will bend towards the normal (an imaginary line perpendicular to the surface of the medium). This explains the bending of light when observed through a glass of water and a glass of air.

2. What is the index of refraction and how does it relate to Snell's law?

The index of refraction is a measure of how much a medium (such as water or air) slows down the speed of light as it passes through. It is represented by the symbol "n" and is a unitless quantity. The index of refraction is directly related to Snell's law because it determines how much the angle of incidence will change as light travels from one medium to another. The higher the index of refraction, the more light will bend towards the normal.

3. Can Snell's law be applied to other mediums besides water and air?

Yes, Snell's law can be applied to any two mediums that have different indexes of refraction. For example, it can be applied to light traveling from air to glass, or from water to diamond. As long as there is a difference in the density of the two mediums, Snell's law can be used to predict the angle of refraction.

4. How does the thickness of the glass affect the bending of light observed through it?

The thickness of the glass does not have a direct effect on the bending of light observed through it. As long as the glass is uniform in thickness, the light will bend according to Snell's law. However, if the glass has imperfections or is not uniform in thickness, it can cause the light to refract at different angles, resulting in a distorted image.

5. Is the bending of light always the same when observed through a glass of water and a glass of air?

No, the bending of light can vary depending on the angle at which the light enters the medium and the specific properties of the two mediums. For example, light may bend more when traveling from air to glass than it does when traveling from air to water, because glass has a higher index of refraction than water. Additionally, the thickness and quality of the glass can also affect the bending of light. These factors may cause slight variations in the bending of light when observed through different mediums.

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