A refracting telescope has an objective lens with a focal...

A refracting telescope has an objective lens with a focal length of $2.20 \mathrm{~m}$ and an eyepiece with a focal length of $1.5 \mathrm{~cm}$. If you look through this telescope the wrong way, that is, with your eye placed at the objective lens, by what factor is the angular size of an observed object reduced?

Key Concepts

Focal Length

Focal length is a measure of how strongly an optical element, such as a lens, converges or diverges light. In a telescope, the focal length of the objective determines how much light is gathered and how the image is formed, while the focal length of the eyepiece affects the scale of the magnified image. The ratio of these focal lengths is fundamental to the calculation of the telescope's magnification.

Reversed Telescope Configuration

Viewing a telescope in reverse, that is, placing your eye at the objective rather than at the eyepiece, inverts the usual angular magnification. Instead of magnifying the image, the telescope reduces the angular size by a factor equal to the ratio of the eyepiece’s focal length to the objective’s focal length. This inverse relationship is essential when considering the effect of using the telescope in a non-standard configuration.

Angular Magnification

Angular magnification is the ratio of the apparent angular size of an object when viewed through an optical instrument to the angular size when viewed with the naked eye. In telescopes, this is determined by the division of the focal lengths of the objective and the eyepiece, and it tells us by what factor the instrument enlarges or reduces the view of an object.

Refracting Telescope

A refracting telescope uses lenses to bend (refract) light in order to form an image. It typically consists of an objective lens, which gathers light from a distant object, and an eyepiece, which magnifies the image formed by the objective. The performance of the telescope is largely dependent on the properties and focal lengths of these two lenses.

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