A certain telescope has an objective mirror with an aperture...

A certain telescope has an objective mirror with an aperture diameter of $200 \mathrm{~mm}$ and a focal length of $2000 \mathrm{~mm}$. It captures the image of a nebula on photographic film at its prime focus with an exposure time of $1.50 \mathrm{~min}$. To produce the same light energy per unit area on the film, what is the required exposure time to photograph the same nebula with a smaller telescope, which has an objective lens with an aperture diameter of $60.0 \mathrm{~mm}$ and a focal length of $900 \mathrm{~mm} ?$

Key Concepts

Aperture

The aperture of a telescope is the diameter of its primary light?collecting element (mirror or lens). It determines how much light from celestial objects is gathered, with larger apertures capturing more light, which is crucial for observing faint objects and reducing required exposure times.

Focal Length and f-Number

The focal length, in combination with the aperture, defines the f-number (or focal ratio) of the telescope (calculated as focal length divided by aperture diameter). The f-number influences the brightness of the image at the focus; lower f-numbers yield brighter images. This concept is critical because the exposure time needed is not just a function of the aperture area but also how the collected light is distributed over the image, which is determined by the f-number.

Exposure Time

Exposure time is the duration for which the imaging medium is exposed to light. In astrophotography, it is adjusted based on the telescope’s light gathering properties so that the same amount of light energy per unit area is recorded. When using a telescope with a smaller aperture or a higher f-number, longer exposure times are required to compensate for less light per unit time reaching the focal plane.

Light Gathering Power

The light gathering power of a telescope is directly related to the area of its aperture, which scales with the square of the diameter. A larger aperture collects more light per unit time than a smaller one, meaning that for a given celestial object, a telescope with a smaller aperture requires a longer exposure time to achieve the same brightness on the imaging medium.

Transcript

Please give Ace some feedback