Ophthalmic prisms are thin prisms with an apical angle of less than 10-15 degrees. They are used in refractive corrections and can be prescribed for conditions like strabismus. The orientation of a prism, whether base-in or base-out, affects how the eye perceives an object through the prism. Prism power can be calculated using formulas like Prentice's rule and decompounded or recombined as needed for a prescription.