A pentaprism is a five-sided reflecting prism used to deviate a beam of light by 90◦ without inverting an image. Pentaprisms are used in the viewfinders of SLR cameras.
(a) What prism angle β is required for a normal-incidence beam from the left to exit the bottom surface at normal incidence?
(b) If all interfaces of the pentaprism are uncoated glass with index n = 1.5, what fraction of the intensity would get through this system for a normal incidence beam? Compute for p-polarized light, and include transmission through the first and final surfaces as well as reflection at the two interior surfaces.
The Attempt at a Solution
a) I really am lost at how to find the prism angle. I know it should come from an angle of deviation calculation but cannot set one up.
b) The overall transmission through the device is the repeated application of the Fresnel equations at each point mentioned: the transmittance from air to glass at normal incidence: 96 % I_o. Then the reflectance at the angle required for total internal reflection twice (this is 41 degrees), and finally transmittance from glass to air again.
Is solution process correct?