Snell's Law HELP TEST TOMMOROW

In summary, Snell's Law is an equation used to calculate the angles and indices of refraction when light passes through different mediums. To find the angle of refraction, one needs to use the inverse sin (sin^-1) function to "undo" the sin component of the equation. This can be done by applying the inverse sin to both sides of the equation.
  • #1
bflatt
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Snell's Law HELP! TEST TOMMOROW!

Homework Statement



Hi, I have a problem with Snell's Law...i understand that it is:
n1(sin)theta1 = n2(sin)theta2

but for the test, we need to know how to manipulate the problem to find the angle of refraction...i will have a calculator to plug thing in but i just don't understand how to! Apparently after you find one thing you need to use an inverse sin (sin-1) or something...PLEASE HELP!

An example problem for this is:
A Beam of light passes from glass (n=1.51) to an unknown medium X (nX=?).
If the angle of incidence is 40 and the angle of refraction is 29 then the index of refraction of the unknown medium is closest to:
a)1.17, b)1.38, c)1.63, d)1.83 or e)2.00

Followed by: The beam of light exists medium X and enters air. If it has an incident angle of 29 at the X-Air boundary, find the angle of refranction in the air?



The Attempt at a Solution


for example my notes say: Nw(sin)theta W = Na(sin)theata A
w=water=1.333
a=air=1
1.333(sin)theta W=1 x sin(37)(angle of incidence)
sin thetaW=sin(37)/1.333
Theta W= (sin -1)/(inverse sin) [sin(37)/1.333]

WHY IS IT GO FROM SIN(theta W) TO INVERSE SIN!?

I Know there is a lot fo questions and info here...these are questoins from a quiz i did and i did very poorly...my test is tommorow and help would be greatly appretiated THANKS SOOO MUCH!
 
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  • #2
To explain the inverse trig function part:

Starting with this line of your example:

sin(theta_w)=(sin37/1.333)

The sin^-1 (or inverse sin, also called arcsin) is just a function that you use to "undo" the sin(theta_w) to get just theta_w. You apply it to both sides of your equation like you would anything else when trying to isolate a variable. So you would have

sin^-1{sin(theta_w)} = sin^-1{sin37/1.333}

the left side then becomes just theta_w, and by calculating the right side you get the angle of refraction.
 
  • #3
ooooo thanks so much...the test was still REALLY hard but what can you do...thanks a ton i appreatiate it
 

1. What is Snell's Law?

Snell's Law is a principle in physics that describes the relationship between the angle of incidence and angle of refraction for a ray of light passing through two different media with different refractive indices.

2. How is Snell's Law written mathematically?

Snell's Law is written as n1sinθ1 = n2sinθ2, where n1 and n2 are the refractive indices of the two media and θ1 and θ2 are the angles of incidence and refraction, respectively.

3. What is the significance of Snell's Law?

Snell's Law helps us understand how light bends when it passes through different materials, such as air, water, or glass. It is also used in various applications, such as lenses, prisms, and fiber optics.

4. How is Snell's Law used in everyday life?

Snell's Law is used in everyday life in various ways. For example, it helps us understand why objects appear distorted when submerged in water, why rainbows form, and how corrective lenses in glasses or contact lenses work.

5. How can I apply Snell's Law to solve problems?

To apply Snell's Law to solve problems, you need to identify the relevant variables (refractive indices and angles) and substitute them into the equation. Then, you can solve for the unknown variable. It is important to use the correct units and remember that the angles must be measured relative to the normal line.

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