Geometric optics - thickness of acrylic ?

[carnivalcougar]

Homework Statement

A ray is deflected by 2.37cm by a piece of acrylic. Find the thickness t of the acrylic if the incident angle is 50.5 degrees.
http://imgur.com/kx2VT5c

Homework Equations

n1sinΘ1 = n2sinΘ2

The Attempt at a Solution

n of acrylic is 1.5. Therefore, the refracted angle is 30.958 degrees. ( 1(sin(50.5)) = 1.5(sin(θ)) )

I'm not sure if I can make a triangle within the acrylic that is above the ray line where one angle is 50.042, one is 90, and the other is 30.958 and use 2.37cm as on side of the triangle.

 

[SammyS]

Homework Statement

A ray is deflected by 2.37cm by a piece of acrylic. Find the thickness t of the acrylic if the incident angle is 50.5 degrees.
http://imgur.com/kx2VT5c

Homework Equations

n1sinΘ1 = n2sinΘ2

The Attempt at a Solution

n of acrylic is 1.5. Therefore, the refracted angle is 30.958 degrees. ( 1(sin(50.5)) = 1.5(sin(θ)) )

I'm not sure if I can make a triangle within the acrylic that is above the ray line where one angle is 50.042, one is 90, and the other is 30.958 and use 2.37cm as on side of the triangle.

Break this up into two triangles.

What is the distance that the ray travels through the acrylic ?
...

 

[carnivalcougar]

The distance that the ray travels through the acrylic is the hypotenuse of a triangle I can make using 2.37cm as one side. However, I do not know how to find the angles of this triangle

 

[SammyS]

The distance that the ray travels through the acrylic is the hypotenuse of a triangle I can make using 2.37cm as one side. However, I do not know how to find the angles of this triangle

What angle does that hypotenuse make with the normal?

What angle does the exit ray make with the normal?

 

[carnivalcougar]

The exit ray makes an angle of 50.5 with the normal while the refracted ray makes an angle of 30.958 with the normal.

I drew which triangle I am talking about on the diagram.

 

[SammyS]

The exit ray makes an angle of 50.5 with the normal while the refracted ray makes an angle of 30.958 with the normal.

I drew which triangle I am talking about on the diagram.

What is the complimentary angle to the 50.5° angle you have drawn ?

 

[carnivalcougar]

That would be 39.5 degrees

 

[SammyS]

That would be 39.5 degrees

Rotate that angle 90° counter-clockwise.

Where does it now line up ?

 

[carnivalcougar]

I think it would be south of the X axis. Which would give me the angle I need to find the third angle of the triangle?

 

[SammyS]

I think it would be south of the X axis. Which would give me the angle I need to find the third angle of the triangle?

Yes.

 

[carnivalcougar]

Would I then use the law of sines to find the hypotenuse of this triangle?

Thanks!

 

[SammyS]

Would I then use the law of sines to find the hypotenuse of this triangle?

Thanks!

You have to add the 39.5° angle to the angle of refraction.

Then use the definition of the cosine to find the hypotenuse. Right?

 

[carnivalcougar]

Oh yeah that would have been easier. Either way I got 7.0852 for the hypotenuse. Then I used the law of sines on the triangle that has the same hypotenuse but the opposite side is the normal line, and therefore, the thickness of the acrylic to find what the thickness of the acrylic is. This came out to be 6.07587cm.

 

[SammyS]

Oh yeah that would have been easier. Either way I got 7.0852 for the hypotenuse. Then I used the law of sines on the triangle that has the same hypotenuse but the opposite side is the normal line, and therefore, the thickness of the acrylic to find what the thickness of the acrylic is. This came out to be 6.07587cm.

Good !