A shaft of light pass through the prism

[thee]

A shaft of light passes through a prism with refracting angle \theta and refractive index n. Let \alpha be the deviation angle of the shaft. Demonstrate that if the shaft of light passes through the prism symetrically the angle \alpha is the least?

 

[topsquark]

A shaft of light passes through a prism with refracting angle \theta and refractive index n. Let \alpha be the deviation angle of the shaft. Demonstrate that if the shaft of light passes through the prism symetrically the angle \alpha is the least?

The least in regards to what?

-Dan

 

[thee]

picture

I suppose that \beta is the refracting angle

I think that it try to proove that \beta is equal to \theta angle \alpha will become the least.

 

[lightgrav]

"passes through symmetrically" means that the path inside the prism
is parallel to the face of the prism that isn't used as a window ...
that is, theta_glass on face 2 = - theta_glass on face 1.

You'll probably want to assume an "apex" angle for the prism
and recall that the interior angles in a triangle sum to 180,
to relate the theta_glass on face 2 to the theta_glass on face 1.

With the deflection angle as a function of theta_glass, set the derivitive =0.