Optical Instruments - Telescope

An optical instrument that uses objective and eye piece lenses to magnify distant terrestrial or celestial objects is called a telescope.

1. \[\mathrm{M_{D.D.V}=\frac{f_{o}}{f_{e}}\left(1+\frac{f_{e}}{D}\right)}\]
2. M = \[\frac{\mathrm{f}_{0}}{\mathrm{f}_{0}}\]

• Telescopes are used to see terrestrial or astronomical bodies.
• A telescope essentially uses two lenses, or one large parabolic mirror and a lens.
• The lens facing the object is called the objective.
• The objective is kept with as large an aperture as possible.
• In Newtonian telescopes, a large parabolic mirror faces the object.

Terrestrial telescope

• Terrestrial telescopes are used to observe objects on Earth, such as mountains, trees, or players in a stadium.
• In this case, the final image must be erect.
• The eye lens used for this purpose must be concave, and such a telescope is popularly called a binocular.
• A variety of binoculars use three convex lenses with proper separation.
• The third lens again inverts the second intermediate image, making the final image erect with respect to the object.

Astronomical telescope

• Astronomical telescopes are used to observe planets, stars, galaxies, and other distant heavenly bodies.
• In this case, there is no necessity for an erect image.
• Such telescopes use a convex lens as the eyepiece.

• It is used to view distant objects.
• The objective lens has a large focal length.
• The objective lens forms the image at its focus, and this image acts as the object for the eyepiece.
• The eyepiece forms the final virtual, magnified image.

Objects seen through a telescope cannot be brought to the least distance of distinct vision from the objective in the way they can be in microscopes. For telescopes, the object's visual angle is measured from its own position, which is effectively at infinity. The visual angle of the final image is β, and its position may be adjusted to D. Under normal adjustment, the final image is at infinity and subtends a greater visual angle than the object.

Working idea

• The beam of incident rays is inclined at an angle α\alphaα with the principal axis.
• The emergent beam is inclined at a greater angle β\betaβ with the principal axis.
• This produces angular magnification.

Formation of an image

• The objective of focal length f_o​ focuses the parallel incident beam at a distance f_o​ from the objective.
• This forms an inverted intermediate image.
• For normal adjustment, the eyepiece is adjusted so that the intermediate image lies at the eyepiece's focal length.
• The rays refracted beyond the eyepiece form a parallel beam inclined at an angle β with the principal axis.
• Therefore, the final image is also at infinity

• Resolving power is the ability to produce distinct images of two closely spaced objects.
• The angular separation between two resolvable objects is given by Rayleigh's criterion.
  sin⁡ θ = 1.22\[\frac {λ}{d}\]
• Here, d is the aperture.
• Resolving power is the inverse of angular separation.
• A larger aperture gives better resolving power.

• Modern telescopes often use a concave mirror rather than a lens for the objective.
• Telescopes with mirror objectives are called reflecting telescopes.
• There is no chromatic aberration in a mirror.
• Mechanical support is less difficult because a mirror can be supported over its entire back surface.
• A reflecting telescope may use another mirror to deflect the focused light.
• In a Cassegrain telescope, a convex secondary mirror focuses the light so that it passes through a hole in the primary mirror.
• This arrangement provides a large focal length in a short telescope.