Friday

February 27, 2015

February 27, 2015

Posted by **Reiny** on Thursday, April 19, 2007 at 6:08pm.

Snell's Law says

sin(angle of incidence)/sin(angle of reflection) = refractive index

since you know the two angles...

sin45/sin27 = refractive index

=1.5575365

so for an angle of refection of 25º

sin(incidence angle)/sin25º=1.5575..

sin(incidence angle)=sin25(1.55..)

=.6582433

so angle of incidence = arcsin(.658..)

=41.166º

That's just the application of Snell's, that part I've done. What I need is:

sin(a)/sin(a-25) = RI

I would solve it by iteration. There is no simple solution to it.

OH...you could graph it on a calculator and see where it crosses the axis. Plot y as a function of x on your graphing calculator.

y= RI - sin x /sin(x-25)

use sin(A-B)=sinAcosB - cosAsinB

sin(a-25)=sina(cos25) - cosa(sin25)

=.9063sina -.4226cosa

so in sina/sin(a-25)=RI

sina = .9063(RI)sina - .4226(RI)cosa

sina - .9063(RI)sina = -.4226cosa

sina(1-.9063(RI)) = -.4226cosa

sina/cosa = -.4226/1-.9063(RI))

Tana = ........

a = arctan(.....)

Hi!!

I'm a hobby gem faceter and am trying to figure out some of the math involved. What I want to know is assuming I have a piece of glass, refractive index of 1.54 (or anything for that matter) at what angle would the light need to enter it to be deviated by a certain amount?

For instance, using Snell's law, I know that if a beam of light goes into glass at a 45 degree angle (from the norm), it will travel through the glass at about 27 degrees. The light has deviated by 18 degrees. What angle would I need it to enter if I wanted it to deviate by 25 degrees?

Thanks for any help.

**Answer this Question**

**Related Questions**

math - Snell's law of refraction can be written as sin i = n sin r, where n is ...

Physics Word Problem - using Snell's Law (sin(theta1)/sin(theta2) = v1/v2 where...

Physics Word Problem - using Snell's Law (sin(theta1)/sin(theta2) = v1/v2 where...

math - Snell's law of refraction can be written as sin i = n sin r, where n is ...

Physics (Please check) - Calculate the index (n water) of refraction of water ...

physics - light travels from ethanol intro crown glass. what's the brewster ...

Physics - All answers should be in degrees. (a) Using the result of Lecture 31 ...

Physics - A ray of light stikes a flat 2 cm thick block of ice (n=1.5) at an ...

physics - 1.A beam of light passes through the air and enters a diamond at an ...

Physics - A beam of light is incident on the surface of clear ice at 60 degrees ...