General Physics (Light Refraction)

[mooeypoo]

Hey guys,

 

I have a hw question I am stumped on, and I need help.

 

I did most of it, so I'm going to post the question and what I did do; my problem is the last part of finding "d".

 

The Question:

When the light illustrated in the figure passes through the glass block, it is shifted laterally by the distance d. Taking n=1.50, find the value of d.

 

Illustration:

((i have a few problems for some reason... if it doesn't load, the illustration is here))

 

 

My partial solution:

n1*sin(theta1)=n2*sin(\theta2)

 

n1=1.000 (in air)

n2=1.5 (given)

 

so:

 

sin(theta2)=sin(30)/1.5

theta2=19.47 deg

 

theta3 (emerging) is 30 degrees again (the same formula reversed).

 

I calculated the distance I called "X" (bottom of the triangle inside the glass box) ->

 

x= 2.00cm * tan(19.47) = 0.707 cm

 

.... but now what?

 

I tried rotating the triangles, putting them one next to the other, switching, flipping.... bah. How do I find d ??

 

Thanks in advance,

 

~moo

 

(p.s: I *tried* using LaTeX but I failed miserably... all the help I found was results, not 'how tos' so... if you post a LaTeX version of the answer, I'd appreciate a short example of what command u did before that).

[swansont]

You can draw another right triangle that has "d" as one leg and the dotted line as another. The apex angle has to be 30º - 19.47º You have enough information to find the hypotenuse, since it will also be the hypotenuse of the other triangle (apex angle 19.47º and one side 2 cm). That should give you enough to solve for d.

[mooeypoo]

You can draw another right triangle that has "d" as one leg and the dotted line as another. The apex angle has to be 30º - 19.47º You have enough information to find the hypotenuse, since it will also be the hypotenuse of the other triangle (apex angle 19.47º and one side 2 cm). That should give you enough to solve for d.

 

... oh RIIIIGHT they share hypothenuses.. (hypotheni?)

 

JEESH! I was trying to find anything that is similar between them (I actually calculated that angle you were talking about 30-19.47 but had no idea where to go from there)

 

I feel dumb now

 

Thanks

 

~moo