Snells Law (Changing view of an object through different materials)

In summary, you tried to solve Snell's law but were unsuccessful. You followed a different path that used the side of the triangle to get rid of the hypotenuse.
  • #1
rzermatt
8
0
[SOLVED] Snells Law (Changing view of an object through different materials)

Homework Statement


A shallow glass dish is 4.0cm wide at the bottom, as shown in the attached figure. When at observer's eye is positioned as shown, the observer sees the edge of the bottom of the empty dish. When this dish is filled with water, the observer, with the eye positioned as before, sees the center of the bottom of the dish. Find the height of the dish.

Image:
img294.imageshack.us/img294/8576/prblmqp0.jpg

Homework Equations


Snell's Law:
n1 * sin(theta1) = n2 * sin(theta2)

n(water) = 1.333
n(air) = 1.000

The Attempt at a Solution


My attempt at the solution was futile. I can't seem to find a way to put the variable of height into Snell's law without being able to solve it. For example, I tried:

1.333(sin(arcsin(h/2)) = 1.000*(sin(arcsin(h/4))

But of course that would not work! How can I switch the variables up? Or am I trying to solve this the wrong way? Any help would be much appreciated.
 
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  • #2
Hi rzermatt,

You had Snell's law as:

[tex]
1.333 \sin(\theta_i) = 1.000 \sin(\theta_r)
[/tex]

and you saw that [itex]\theta_i[/itex] was the top vertex of the triangle with bottom side of 2 cm.

Instead of inserting arc-functions, I think it might be better to follow this path: In terms of the sides of the triangle, what is [itex]\sin\theta_i[/itex]? This will put the hypotenuse of each triangle in your equation, but go ahead and label them and put them in; then the trig functions will be gone.

Then, use the relationship between the hypotenuse of these triangles and their sides to get rid of the hypotenuse of each triangle. What do you get?


(By the way, the problem with the equation you gave is that it is the tangent of the angle that relates the sides h and 2, and sides h and 4, so your equation would need to be:

1.333 * sin(arctan(2/h) ) = 1 * sin(arctan(4/h)
 
  • #3
That worked out great! I used the Pythagorean theorem to fix the relationships and then eliminate all the trig all together.

Thanks for the help!
 

What is Snell's Law?

Snell's Law, also known as the Law of Refraction, describes the relationship between the angle of incidence and the angle of refraction when a light ray passes through a boundary between two different transparent materials.

What is the formula for Snell's Law?

The formula for Snell's Law is n1sinθ1 = n2sinθ2, where n1 and n2 are the refractive indices of the two materials, and θ1 and θ2 are the angles of incidence and refraction, respectively.

How does changing the angle of incidence affect the angle of refraction?

As the angle of incidence increases, the angle of refraction also increases. This means that the light ray is bent more as it passes through the boundary between the two materials.

What is the critical angle in Snell's Law?

The critical angle is the angle of incidence at which the angle of refraction is 90 degrees. This occurs when the light ray passes from a more dense material to a less dense material.

What is the practical application of Snell's Law?

Snell's Law is used in many fields, including optics, engineering, and physics. It is particularly important in designing lenses and prisms for optical devices such as cameras and microscopes.

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