An astronomical telescope combines two lenses, called the objective lens and the eyepiece, spaced at a distance. It is used to observe distinctive images of celestial bodies such as stars and planets. It is the ratio of the angle 𝛽 subtended at the eye by the image to the angle ⍺ subtended at the eye by the object representing the magnifying power(m) of a telescope. 

Telescope

• The telescope is often used to magnify distant objects by providing angular magnification.
• There is also an objective and an eyepiece. However, the objective has a significantly longer focal length and a much greater aperture than the eyepiece in this case.
• Light from a distant object enters the objective, forming a true picture in the tube’s second focal point.
• The picture is magnified by the eyepiece, resulting in an inverted image.

Astronomical telescope and magnifying powers 

• An astronomical telescope is a refracting telescope used to observe celestial things such as stars, planets, and satellites.
• It comprises two converging lenses coaxially positioned at the outer ends of two moving tubes.
• The major factors for an astronomical telescope are its light-gathering power and its resolution or resolving capability. The former certainly depends on the scope of the objective.
• Smaller dimensions allow for the observation of fainter objects. The diameter of the target also influences the resolving power, or the capacity to distinguish two things that are in extreme proximity to one another.
• As a result, the preferred goal of optical telescopes is to create them with big diameter objectives.

Working of an astronomical telescope

• It comprises two lenses: the objective lens O, which has a long focal length and a big aperture, and the eyepiece E, which has a short focal length and a tiny aperture. The magnification occurs due to the refraction through these lenses.
• The final image is created at infinity during typical telescope adjustments.
• The objective creates a real and inverted picture of the faraway subject at its focal plane. When the eyepiece’s distance from the objective is changed, the final image is generated with the least distance vision. The eye location is adjusted to create the final picture at infinity.
• In normal adjustment, the focal length of the objective lens should be large, and the focal length of the eye lens should be small to maximise the magnifying power of an astronomical telescope.

Combination of lenses

• The combination of lenses facilitates the creation of diverging or converging lenses with the necessary magnification.
• It also improves the sharpness of the image.
• As the picture of the first lens becomes the subject for the second, the overall magnification of the arrangement is a product of the magnification of the constituent lenses.
• Hence, overall magnification m of a combination of lenses is given by

m = m1.m2.m3… and so on.

• A lens combination system is often used to create lenses for camera systems, microscopes, telescopes, and other optical instrumentation.

Magnifying powers

• Magnifying power is defined as the angle subtended by the final picture at the eye, given by 𝛽, relative to the angle subtended by the object at the lens or eye, given by ⍺. 

m = 𝛽/⍺ = (h/fe)/(fo/h)

Thus, m = fo/fe

• Magnifying power:

When the final image is formed at least distance of distinct vision (D), then

m = fo/fe {1+ (D/fe)} where fo and fe are focal lengths of objective and eyepiece, respectively.

Length of the telescope (L) = (fo + ue)

where ue = distance of the object from the eyepiece.

• When the final image is formed at infinity, then m = fo/fe

Length of the telescope (L) = fo + fe

For a higher magnifying power, fo should be large, and fe should be small.

Conclusion

A telescope used to view distant objects in the sky—such as the stars, planets, and satellites—is known as an astronomical telescope. An astronomical telescope can have reflective mirrors or refractive lenses to magnify the distant object. There is an objective lens with a large focal length (fo) and large aperture and an eye lens with a small aperture and focal length. The magnification power of an astronomical telescope is the ratio of the focal length of the objective to the focal length of the eyepiece.