Plan, plan fluorite, and plan apochromatic (apo) objectives are types of microscope objectives that are designed to provide high-quality images with minimal distortion and aberration. The main difference between these objectives is the type and number of lenses they contain and the level of correction they provide for chromatic and spherical aberration.

1. Plan objectives: These are the most basic type of microscope objectives and are designed to provide a flat field of view. They contain a single lens element and are typically used for brightfield microscopy. This is the most common style of objective and very affordable

2. Plan fluorite objectives: These objectives are similar to plan objectives but contain a fluorite element, which is a type of crystal that has a low refractive index and is highly resistant to chromatic aberration. Fluorite objectives are more expensive than plan objectives but provide improved image quality and resolution.

3. Plan apochromatic (apo) objectives: These are the most advanced type of microscope objectives and are designed to provide the highest level of correction for chromatic and spherical aberration. They contain multiple lens elements, including one or more special apochromatic elements, and are used for demanding applications that require high-resolution images with minimal distortion. Apo objectives are the most expensive type of objectives but are widely considered to be the best available in terms of image quality.

In summary, plan, plan fluorite, and plan apo objectives are differentiated by the type and number of lenses they contain and the level of correction they provide for chromatic and spherical aberration. Plan objectives are the most basic and least expensive, while apo objectives are the most advanced and expensive.