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 derivative =0.