If you look at stars with binoculars with lenses about 8 cm (3 inches ) in diameter, how many t

Name: Problem 1, Chapter 27: Pathways to Astronomy
Uploaded: 2020-02-16T21:51:17-08:00
Duration: 1 min 19 s
Channel: Carlos Henrique De Lima
Description: If you look at stars with binoculars with lenses about 8 cm (3 inches ) in diameter, how many times fainter a star should you be able to see compared to what you can see with your unaided, fully dilated eye, with the pupil open to about 8 mm ?

step 1 In this problem, we want to know what is the magnification of an astronomical telescope. Both ob

Question

If you look at stars with binoculars with lenses about $8 \mathrm{cm}$ $(3 \text { inches })$ in diameter, how many times fainter a star should you be able to see compared to what you can see with your unaided, fully dilated eye, with the pupil open to about $8 \mathrm{mm}$ ?

   If you look at stars with binoculars with lenses about $8 \mathrm{cm}$ $(3 \text { inches })$ in diameter, how many times fainter a star should you be able to see compared to what you can see with your unaided, fully dilated eye, with the pupil open to about $8 \mathrm{mm}$ ?

Pathways to Astronomy

Stephen E. Schneider 2nd Edition

Chapter 27, Problem 1

Instant Answer

Solved by Expert Carlos Henrique De Lima

02/16/2020

Step 1

The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius. For the binocular lenses, the diameter is 8 cm, so the radius is 4 cm. Show more…

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If you look at stars with binoculars with lenses about $8 \mathrm{cm}$ $(3 \text { inches })$ in diameter, how many times fainter a star should you be able to see compared to what you can see with your unaided, fully dilated eye, with the pupil open to about $8 \mathrm{mm}$ ?

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Key Concepts

Relationship Between Diameter and Area

Since the area of a circular aperture is calculated as ? times the square of the radius (or equivalently, proportional to the square of the diameter), when comparing instruments with different diameters, the increase in light collection—and therefore the ability to see fainter objects—is given by the square of the ratio of their diameters. This concept is fundamental in understanding how optical devices enhance observational capabilities compared to unaided vision.

Aperture and Light Gathering Area

The light gathering power of an optical instrument is determined by the area of its aperture, which is proportional to the square of its diameter. This means that larger apertures can collect more light, allowing fainter objects to be seen. In the context of comparing binoculars to the human eye, the relative brightness detection depends on the ratio of the areas of their apertures.

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