# A shaft of light pass through the prism

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?

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thee said:
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

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.

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lightgrav
Homework Helper
"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.