An equilateral triangular glass prism has an index of refraction of 1.52. Calculate the angle of incidence at which a ray of light would traverse the prism symmetrically (the angle of emergence equal to the angle of incidence).
please help..thankss
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An equilateral triangular glass prism has an index of refraction of 1.52. Calculate the angle of incidence at which a ray of light would traverse the prism symmetrically (the angle of emergence equal to the angle of incidence).
please help..thankss
If you draw a diagram of the triangle, you see that one has symmetry only if the segment of the ray's path within the prism is parallel to one side of the prism (the side through which it doesn't pass), leading to an angle of refraction of 30°. Thus, we use Snell's law (with the refractive index of air being approximated as 1):
$\displaystyle n_1\sin\theta_1=n_2\sin\theta_2$
$\displaystyle 1\cdot\sin\theta_1=1.52\sin{30^{\circ}}$
$\displaystyle \sin\theta_1=1.52\cdot\frac{1}{2}$
$\displaystyle \sin\theta_1=0.76$
Your calculator should give you the answer to that.
--Kevin C.
