Light Refracted through a Prism?

Question

Light is incident along the normal to face AB of a glass prism of refractive index 1.58, as shown in the figure

Find alpha_max, the largest value of the angle alpha such that no light is refracted out of the prism at face AC if the prism is immersed in air.

image :http://session.masteringphysics.com/problemAsset/1011229/12/yf_Figure_33_36.jpg

unfortunatley the answer and method at http://answers.yahoo.com/question/index;_ylt=AhEICGcxKuOZPVtmXQg9weFIzKIX;_ylv=3?qid=20070409080954AAZfvRi

is incorrrect

Answer 1

The light passes undeviated through face AB

When it arrives at face AC, it must make the "critical angle " with the normal there

To find the critical angle "c" for this glass:-

            refractive index   =   1 / sin (c)

                                      1.58   =   1 / sin(c)

                   sin(c)   =   1 / 1.58   =   0.6329

  So angle c   =   39.26 degrees.

This makes angle alpha   =   90  -  c   =   90  -  39.26

    Angle  alpha    =    50.74  degrees.