A telescope is an afocal system: parallel light in, parallel light out. It magnifies by increasing the angle that a distant object subtends at the eye
It has two lenses

The objective, a weaker plus lens facing the object
The eyepiece (ocular), a stronger lens next to the eye

The lenses are separated so that the second focal point of the objective coincides with the first focal point of the eyepiece. Gullstrand's equation then gives an equivalent power of zero (see Thick Lenses and Lens Systems)
Angular magnification M = −F_e ÷ F_o = −f_o ÷ f_e

## Galilean telescope

Plus objective, minus eyepiece
Separation = f_o − |f_e|: the eyepiece intercepts the converging light before it focuses
The image is erect, because F_e is negative so M is positive
Short and light, but with a narrow field of view and limited magnification (usually up to about ×4)
Worked example: objective +10D, eyepiece −30D

M = −(−30) ÷ 10 = ×3, erect
Separation = 10 cm − 3.33 cm = 6.67 cm

Uses: surgical loupes, spectacle-mounted low vision telescopes, and the magnification changer of the operating microscope and slit lamp

A Galilean telescope can be made from a high plus spectacle lens and a high minus contact lens. It is occasionally used as a low vision aid, giving magnification without a spectacle-mounted telescope.

## Keplerian (astronomical) telescope

Plus objective, plus eyepiece
Separation = f_o + f_e. The objective forms a real, inverted intermediate image at the shared focal plane
The final image is inverted (M is negative). Erecting prisms, such as a pair of Porro prisms, are added to correct this (see Prisms)
Longer, but with a wider field, better image quality and higher magnification than a Galilean telescope
Worked example: objective +10D, eyepiece +40D

M = −40 ÷ 10 = ×4, inverted
Separation = 10 cm + 2.5 cm = 12.5 cm

Uses: binoculars, prismatic surgical loupes, and the eyepieces of slit lamps and operating microscopes

## Telescopes in clinical use

Disadvantages

A narrow field of view, which shrinks as magnification increases
Movements are magnified, so the image appears to swim
A short depth of field

For near objects, the eye must accommodate (or a reading cap is added) by about M² times the vergence of the object

Worked example: viewing an object 1 m away (1D) through a ×2 telescope needs about 4D of accommodation

An uncorrected ametrope can focus a telescope by changing the lens separation (as with binoculars), but this changes the magnification slightly

## The loupe (simple magnifier)

A plus lens with the object at or inside its first focal point forms a virtual, erect, magnified image
Its magnification is compared with viewing the object unaided at the standard near point of 25 cm (4D)

Object at the focal point, image at infinity: M = F ÷ 4
Image at 25 cm, with the eye close to the lens: M = F ÷ 4 + 1. Manufacturers often quote this larger figure

Worked example: a +20D magnifier gives ×5 with the image at infinity, or ×6 with the image at 25 cm
Stand and hand magnifiers, high-add reading spectacles and the direct ophthalmoscope all use this principle (see direct ophthalmoscope and low vision aids)

Surgical loupes are small telescopes, not simple magnifiers: Galilean designs at about ×2–3.5, and prismatic Keplerian designs at higher powers. Higher magnification means a smaller field of view and depth of field, and a fixed working distance.