Optical Magnifiers: Principles of Virtual Image Formation

The Lens: Virtual and Augmented Images

Optical Instrument Functionality

An optical instrument is a subjective device designed to provide an enlarged image of small, nearby objects, allowing for better appreciation of their fine details. The accommodative ability of the human eye is limited by its near point (pr) and far point (pp).

Magnification Principles

• Visual Increase: Provides maximum growth at the near point (pp).
• Ratio: Defined by the apparent angular size of the image provided by the lens versus the angular size of the object at the near point.
• Retinal Images: Calculated as the quotient between the sizes of retinal images.

Magnification depends on the focal length (f'), the eye position relative to the magnifying glass, and the object position at the near point. If two different people use the same lens, the final image size may have the same angle, but the magnification will differ based on their individual near points.

Normal Magnification and Viewing Distance

If the object is at the focal point (PFO) or the image is at the near point (PFI), the increase does not depend on the observer's characteristics. Normal magnification corresponds to an object position of 250mm, considered the standard comfortable reading distance. A smaller increase occurs with a larger focal length.

Equivalent viewing distance is the distance measured from the axial center of the eye where the object should be situated to subtend the same angle as the image through the lens.

Transversal Field and Pupil Dynamics

The transversal field is the portion of the object visible through the lens. Key factors include:

• Pupil of the eye (ps): Given in object space.
• Lens (LS): Given in object space.
• Ideal conditions: When the eye is close to the lens, the field of view increases.

Depth of Focus and Resolving Power

Depth of focus is the axial range of the object space whose image coincides with the observer's range of clear vision. This distance decreases as the eye moves closer to the glass, reaching a minimum when the lens is attached to the eye. When at the PFI, the depth of focus depends solely on the amplitude of accommodation (AA) and is independent of refraction.

Brightness: Magnifiers offer very high luminous efficiency.

Resolving power: The ability to discern images of two points close together. The resolving power of the lens-eye coupling is primarily determined by the resolving power of the eye, which increases as visual magnification increases.