In an astronomical telescope, the focal length of objective...

In an astronomical telescope, the focal length of objective lens and eyepiece are $150 \mathrm{~cm}$ and $6 \mathrm{~cm}$, respectively. In case when final image is formed at least distance of clear vision $(D=25 \mathrm{~cm})$. The magnifying power is
(A) 29
(B) 30
(C) 31
(D) 32

Key Concepts

Angular Magnification

Angular magnification is the measure of how much larger an object appears when viewed through an optical instrument compared to the naked eye. It is determined by the ratio of angles subtended by the image and the object, and in many optical systems it depends directly on the focal lengths of the elements involved.

Focal Length

The focal length of an optical component is the distance over which parallel rays of light are brought to a focus. In instruments such as telescopes, the focal lengths of the objective and eyepiece are critical in determining the overall magnification and image quality.

Least Distance of Distinct Vision

The least distance of distinct vision refers to the closest distance at which the human eye can sharply focus on an object, typically taken to be around 25 cm. This concept is important in optical design when adjusting the final image position to ensure comfortable and clear viewing without excessive strain.

Astronomical Telescope Design

Astronomical telescopes are designed to view distant objects by collecting light through an objective lens and magnifying the image with an eyepiece. The performance and usability of these telescopes depend on the arrangement of these elements, with the focal length ratio and the positioning of the final image (whether at infinity or at the near point) playing key roles in determining effective magnification and viewer comfort.

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