How do I find θi and θr?

[Zoey]

Hi,

 

I am supposed to fill in values in a table for θi and θr (I am also supposed to find the sine of θi and θr, but I should be able to do that easily once I figure out how to find those values in the first place). I am only given the values of n₁ being 1.00 and n₂ being 1.50. Just doing a basic search on the internet, it seems like I might need to cross multiply somewhere, but if so, what should I cross multiply? I am being told to use Snell's Law here. The formula for that is n₂/n₁=Sin θi/Sin θr. I am not sure how to apply the formula for both of the values that they are wanting me to find.

 

I would really appreciate it if someone could show me how to find these values!

 

Thanks

 

*Note: If it will be of help, I have a scientific calculator

Edited May 16, 2016 by Zoey

[John Cuthber]

There isn't enough information to answer the question

[Zoey]

There isn't enough information to answer the question

The only information I was given was n₁ and n₂ to fill in the values θr and θi. There is not any information that I was given that I am leaving out.

[ajb]

If I am reading this right, you can get as far as

 

[math]\sin \theta_{i} = 1.5 \sin \theta_{r}[/math]?

 

Then you want to solve for the two angles?

 

Well, as it stands you have one equation and two unknowns. We can then write one angle as a function of the other

 

[math]\theta_{i} = \arcsin\left( 1.5 \sin \theta_{r} \right)[/math].

 

You could not throw in a [math]\theta_{r}[/math] and get values for [math]\theta_{i}[/math], maybe the principal inverse is okay, maybe you need to check that this is a physically meaningful solution.

 

Anyway, without more information I am not sure you can do much more.

[Sensei]

If I understood question correctly,

you have table (how many rows?):

so made up couple [latex] \theta_{i}[/latex] (in the right range),

and calculate what will be [latex]\theta_{r}[/latex] corresponding to it,

and fill table with couple such pairs.

 

[Zoey]

 

I have tried to attach an image of the problem, but I don't know if it will work.

Edited May 16, 2016 by Zoey

[Zoey]

Also, if it will help, here is the "Gizmo" (which is like a virtual science lab) that I am supposed to complete to go along with the table I need to fill out.

https://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=608

 

I appreciate everyone who is trying to help with this, and I apologize if I did not give you guys enough information to be able to help.

[Mordred]

Ok well this is definitely a Smells law project.

 

So in that regard you have pieces of information outside what you posted.

 

First is the law of reflection.

[latex]\theta_I=\theta_r[/latex]

The next is the index of refraction.

 

For air the index of refraction is 1.00.

 

So on your table I assume you are given different index of refraction to work with? You give one value n_1 being air but only provided one medium index of refraction for the prism being n_2 equals 1.5

 

Noted your image didn't copy on the site however you can type in the values you are given for each row and type in the columns you need to fill.

 

Note you'll be using the law of refraction.

 

This law can be stated in two parts.

 

1) [latex]n_1*sine\theta_1=???[/latex]

2) what is the relation between [latex]\theta_1 and \theta_2 [/latex]

 

I didn't provide the answers to those two parts as I want you to fill in the blanks.

 

The first part should give you the the detail you need to calculate for your second angle, keeping in mind the second part.

Edited May 17, 2016 by Mordred