A telescope is constructed from two lenses with focal...

A telescope is constructed from two lenses with focal lengths of 95.0 $\mathrm{cm}$ and $15.0 \mathrm{cm},$ the 95.0 -cm lens being used as the objective. Both the object being viewed and the final image are at infinity. (a) Find the angular magnification of the telescope. (b) Find the height of the image formed by the objective of a building 60.0 $\mathrm{m}$ tall and 3.00 $\mathrm{km}$ away. (c) What is the angular size of the final image as viewed by an eye very close to the eyepiece?

A telescope is constructed from two lenses with focal lengths of 95.0 $\mathrm{cm}$ and $15.0 \mathrm{cm},$ the 95.0 -cm lens being used as the objective. Both the object being viewed and the final
image are at infinity. (a) Find the angular magnification of the telescope. (b) Find the height of the image formed by the objective of a building 60.0 $\mathrm{m}$ tall and 3.00 $\mathrm{km}$ away. (c) What
is the angular size of the final image as viewed by an eye very close to the eyepiece?

Key Concepts

Angular Size

Angular size refers to the apparent size of an object as viewed from a particular point, typically measured in radians or degrees. It is calculated by the ratio of the object’s physical size to its distance from the observer. In optical setups, understanding angular size is crucial for assessing how much of an object is captured and how large it appears in the final image.

Focal Length

Focal length is a critical property of lenses and optical systems, defining the distance over which parallel rays of light are brought to a focus. The focal lengths of both the objective and the eyepiece determine how the telescope forms and sizes its images, affecting magnification and image clarity.

Angular Magnification

Angular magnification is a measure of how much larger an optical instrument makes an object appear when viewed through it compared to the naked eye. It is generally determined by the ratio of the focal lengths of the objective and the eyepiece in telescopic systems, and it quantifies the increase in the angular size of the image relative to the object.

Telescope Optics

This concept involves the use of a system of lenses (or mirrors) to collect and focus light from distant objects. In telescopes, the objective lens gathers light and forms an image, which the eyepiece then magnifies so that the details become observable. The design leverages the arrangement and characteristics of multiple lenses to enhance viewing capabilities.

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