I Pentaprism with magnification, which surface is curved?

[nikosb]

I would like to use a pentaprism with some amount of magnification. The pentaprism will be used to reflect a real image at 90 degrees angle but I also want the reflected image to appear larger. The distance between the prism and the real image is about 70cm. The pentaprism has two reflecting sides (surfaces) with mirrored coating and two refracting sides. I understand that one of the four sides needs to be curved (spherical curvature) to achieve the magnification effect. But which of the fours surfaces? Can the reflecting side be curved like a spherical concave mirror? What is the relation between the radius of curvature and the focal length?

 

[Erwinux]

You better use separate lenses to magnify the image. Any curved surface of the pentaprism will cause color aberrations you cannot avoid. Use an achromatic objective and an adequate eyepiece to achieve the magnification you want. The prism should be in between, in the front of the eyepiece. You can use objective and eyepiece from an old binocular. Just find the correct length of the needed tube to get a sharp focused image of the object.

 

[Drakkith]

Any of them can be curved, but you'll generate chromatic and non-chromatic aberrations that may or may not need to be corrected for. Your best bet is probably to place positive lens somewhere in the system. Whether this lens is achromatic or not is up to you since we don't know what tolerances you're dealing with.