Solve Angle of Refraction Problem: Incident 35°, Refracted 22° & Leaving 38°

[aurao2003]

Homework Statement

Hi
I have this little problem bothering. The question goes like this:
A ray enters an equilateral glass prism of refractive index 1.55 at the midpoint of one side of the prism at an angle of inceidence of 35 degrees.
a. Sketch this arrangement and show that the angle of refraction of the light ray in the glass is 22 degrees.
b. Show that the angle of incidence where the light ray leaves the glass prism is 38 degree.
c. Calculate the angle of refraction of the light ray where it leaves the prism.

Homework Equations

n= Sin i/Sin r

The Attempt at a Solution

I am able to do a. For b this is my working:
1.55=Sin i/Sin 22

But I obtained 35.5 degrees. Can anyone please explain where I am going wrong?
Thanks.

 

[tiny-tim]

hi aurao2003!

A ray enters an equilateral glass prism …
…
b. Show that the angle of incidence where the light ray leaves the glass prism is 38 degree.
c. Calculate the angle of refraction of the light ray where it leaves the prism.
…
For b this is my working:
1.55=Sin i/Sin 22

erm … you've misread the question, and probably not drawn the diagram …

b is just geometry … the angle of incidence where the light ray leaves the prism is the angle before it leaves (that's what "incidence" means! ), and you should be able to show that that is 38° …

(and you don't use the sine formula until c)

 

[aurao2003]

Hi
I am trying to do the geometry but its eluding me. Sorry for being slow. But all my A level subjects are self taught. I have got it now. Thanks.
I am doing Maths, Physics and Further Maths!

 

[tiny-tim]

use the theorem that the external angle of a triangle equals the sum of the two opposite internal angles (alternatively, just use the sum of the internal angles equals 180°)

 

[tiny-tim]

perhaps you're not drawing the correct triangle?

draw a line from the bottom right corner to the midpoint of the left side …

then draw the ray: it makes a 35° angle to this line in the air, and a 22° angle through the glass, and hits the bottom of the triangle

you've now two triangles at the bottom of the original triangle: use the 180° rule to find the angle between the ray and the bottom side …

what do you get? ​