The penta prism and half-penta prism are both optical components used to manipulate the orientation and direction of light, but they serve slightly different purposes and have different shapes.

Penta Prism:

• Design: A penta prism is a five-sided prism that deviates the light path by 90 degrees while maintaining the orientation of the image. The entrance and exit faces of the prism are not parallel, which allows the light to be reflected internally by two of the prism's surfaces.
• Function: The penta prism is typically used in applications where it's necessary to redirect light by a specific angle while keeping the image orientation upright. It's commonly used in SLR cameras (single-lens reflex) to direct light from the lens to the viewfinder without inverting the image.
• Key Feature: It ensures that the image remains correctly oriented (upright and laterally correct) even after the light path is bent by 90 degrees.

Half-Penta Prism:

• Design: A half-penta prism is similar in design to a penta prism but with one of the two reflecting surfaces replaced by a transmissive surface, effectively "cutting" the penta prism in half. This results in the light being deviated by only 45 degrees.
• Function: The half-penta prism is used to deviate light by a smaller angle (typically 45 degrees) while still maintaining the orientation of the image. It is often used in situations where space constraints or specific light path requirements make a full penta prism unnecessary or impractical.
• Key Feature: It provides a 45-degree deviation with image orientation correction, but it doesn't offer the full 90-degree deviation of a penta prism.

Summary of Differences:

• Angle of Deviation: The penta prism deviates light by 90 degrees, while the half-penta prism deviates it by 45 degrees.
• Design: The penta prism has five sides and fully reflects light internally, while the half-penta prism is essentially a truncated version with one less reflective surface.
• Application: Penta prisms are often used in optical systems requiring a full 90-degree deviation with image orientation correction, like in cameras. Half-penta prisms are used in applications needing a 45-degree deviation, often where space or design constraints are a factor.

Both prisms ensure that the image remains upright and correctly oriented after light is redirected.

Which is more expensive?

Generally, penta prisms tend to be more expensive than half-penta prisms. The reasons for this include:

1. Complexity and Size: Penta prisms are larger and more complex to manufacture because they involve more surfaces, including two reflecting surfaces that need precise alignment and coating to achieve the correct 90-degree light deviation with minimal distortion.

2. Material and Quality Requirements: High-quality optical glass is used in penta prisms to ensure clarity and minimal light loss, which adds to the cost. The need for precise angles and coatings further increases production costs.

3. Application: Penta prisms are used in high-precision optical instruments like SLR cameras, rangefinders, and other devices where maintaining image orientation with a 90-degree deviation is crucial. These applications often demand high-quality components, driving up the cost.

On the other hand, half-penta prisms, being smaller and simpler with fewer reflective surfaces, are generally less costly to produce. They are often used in less demanding applications, which can also contribute to their lower price.