A refracting telescope is 36.4 cm long and has a 6.0 cm diameter aperture. The magnifying power

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A refracting telescope is 36.4 cm long and has a 6.0 cm...

A refracting telescope is $36.4 \mathrm{cm}$ long and has a $6.0 \mathrm{cm}$ diameter aperture. The magnifying power is $90.0 .$ (a) What are the focal lengths of the lenses? (b) What is the diffraction limit on the minimum angular separation of objects that the telescope can resolve in $500 \mathrm{nm}$ light?

A refracting telescope is $36.4 \mathrm{cm}$ long and has a $6.0 \mathrm{cm}$ diameter aperture. The magnifying power is $90.0 .$
(a) What are the focal lengths of the lenses?
(b) What is the diffraction limit on the minimum angular separation of objects that the telescope can resolve in $500 \mathrm{nm}$ light?

Key Concepts

Refracting Telescope

A refracting telescope is an optical instrument that uses lenses to form images of distant objects. The primary lens, known as the objective, gathers light and forms an image, which is then magnified by a secondary lens called the eyepiece. This configuration is fundamental to understanding optical imaging and astronomical observations.

Focal Length

Focal length is the distance from the lens to the focal point where parallel rays of light converge. In optical systems such as telescopes, the focal length of the objective determines the scale of the image, while the focal length of the eyepiece is crucial for magnification. The relationship between these focal lengths directly affects the overall performance and design of the telescope.

Magnifying Power

Magnifying power, or angular magnification, is a measure of how much larger an object appears when viewed through the telescope compared to the naked eye. It is defined as the ratio of the objective's focal length to the eyepiece's focal length. This concept is essential in optical design because it connects the physical parameters of the telescope to its practical imaging capabilities.

Diffraction Limit and Rayleigh Criterion

The diffraction limit is a fundamental constraint on the resolution of any optical system, arising from the wave nature of light. The Rayleigh criterion provides a practical definition, stating that two point sources can be resolved when the central maximum of one diffraction pattern coincides with the first minimum of the other. This limit, often expressed as 1.22 times the wavelength divided by the aperture diameter, determines the minimum angular separation that can be distinguished.

Angular Resolution

Angular resolution is the smallest angle at which an optical instrument can distinguish two separate light sources. In telescopes, it is primarily limited by diffraction and the size of the aperture. A better angular resolution allows for finer details to be observed, which is critical in many areas of astronomy and imaging technology.

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