Help understanding part of Snell's Law

[Alteaon]

I am studying Snell's law, and there is one part I can't get past in my efforts to understand the whole thing. I'm studying from the Optical Formulas Tutorial by Ellen Stoner, page 23.

Example: If a ray of light travels from air into crown glass, with an angle of incidence of 30 degrees, what will the angle of refraction be? What is the angle of deviation?

incident index: 1
index of refraction of the refracting material: 1.523
angle that the incident light ray makes with the surface: 30
angle that the refracted light ray makes with the surface: ? ( known as r)

(1)(sin 30)=(1.523)(sin r)

sin r= (0.50)/(1.523)

sin r= 0.32830

According to the book, r= 19. How does this happen? How do I go from the sin r =0.32830 to r=19? I can't divide it by sin to get the 19. I'm very frusterated because I am very close to understanding this.

Then 30-19 is 11, which is the angle of deviation, but how do I get from sin r = 0.32830 to r= 19.

I know it's probably obvious for most people, but not for me.:confused:
thank you so so much for any help :)

[Jubilee]

Once you know the sine of an angle, you have the ratio of sides together. You can simply look in a sine table chart to find the answer.

the closest number is .3256 which = sin(19)

making 19 degrees the angle of refraction.

http://www.grc.nasa.gov/WWW/K-12/airplane/tablsin.html

here is a sine table chart :)

[lensgrinder]

sin r = 0.32830
r = sin-1(0.32830)
r = 19.17

Hit 2nd - sin or inv - sin on your calculator.

[Fezz]

Jubilee-

Thanks for the link. This will come in handy.

[HarryChiling]

The diagram below shows how the the angle and it's sides relate.

Sin (angle) = Opposite / Hypotenuse
Cos (angle) = Adjacent / Hypotenuse
Tan (angle) = Opposite / Adjacent

Like lensgrinder mentioned the sin is a ratio of the length of the opposite side of the angle over the hypotenuse of the triangle. Since it is a ratio we know that if you change one side the other is going to change an amount which will keep the ratio the same.

for example sin of 45 degrees is 1/2 or 0.5 which means that the opposite side of the triangle from the angle is 1 unit in length, and the hypotenuse of the angle is 2 units in length. If the opposite side of the angle were 2 units?

0.5 = 2/?
?=4

I hope this helps.

[tmorse]

angle that the incident light ray makes with the surface: 30
angle that the refracted light ray makes with the surface: ? ( known as r)

:)

Angle of incidence and angle of recfraction is ALWAYS measured from the NORMAL to the ray, not the surface.:cheers:

[HarryChiling]

Angle of incidence and angle of recfraction is ALWAYS measured from the NORMAL to the ray, not the surface.:cheers:

Good catch, the angle is measured from normal which is the line perpendicular (90o) from the surface.

[OptiChick21]

Once you know the sine of an angle, you have the ratio of sides together. You can simply look in a sine table chart to find the answer.

the closest number is .3256 which = sin(19)

making 19 degrees the angle of refraction.

http://www.grc.nasa.gov/WWW/K-12/airplane/tablsin.html

here is a sine table chart :)

Yes, now just memorize this chart and any possible test questions will be a snap! LoL. :D

[Fezz]

The Optical Formula Tutorial has a trigonometric table in the back. This should cover it.

[Darryl Meister]

Sine tables are fine, but you'd really just use your calculator, which you're probably allowed to do in most cases. Since SIN Angle = Value then Value = ARCSIN Angle. This means that you would just punch the 'ARCSIN' button (sometimes labeled as SIN-1) on the calculator to get the angle.