Question

Two refracting telescopes are used to look at craters on the Moon. The objective focal length of both telescopes is $95.0 \mathrm{~cm}$ and the eyepiece focal length of both telescopes is $3.80 \mathrm{~cm}$. The telescopes are identical except for the diameter of the lenses. Telescope A has an objective diameter of $10.0 \mathrm{~cm}$ while the lenses of telescope $\mathrm{B}$ are scaled up by a factor of two, so that its objective diameter is $20.0 \mathrm{~cm} .$ a) What are the angular magnifications of telescopes $A$ and $B$ ? b) Do the images produced by the telescopes have the same brightness? If not, which is brighter and by how much?

Name: Problem 76, Chapter 33: University Physics with Modern Physics
Uploaded: 2021-05-22T03:02:23-08:00
Duration: 1 min 1 s
Channel: Narayan Hari

   Two refracting telescopes are used to look at craters on the Moon. The objective focal length of both telescopes is $95.0 \mathrm{~cm}$ and the eyepiece focal length of both telescopes is $3.80 \mathrm{~cm}$. The telescopes are identical except for the diameter of the lenses. Telescope A has an objective diameter of $10.0 \mathrm{~cm}$ while the lenses of telescope $\mathrm{B}$ are scaled up by a factor of two, so that its objective diameter is $20.0 \mathrm{~cm} .$
a) What are the angular magnifications of telescopes $A$ and $B$ ?
b) Do the images produced by the telescopes have the same brightness? If not, which is brighter and by how much?

University Physics with Modern Physics

Wolfgang Bauer, Gary… 2nd Edition

Chapter 33, Problem 76

Instant Answer

Solved by Expert Narayan Hari

05/22/2021

Step 1

The formula for magnification (M) is given by -F_o/F_e, where F_o is the objective focal length and F_e is the eyepiece focal length. Given that F_o = 95 cm and F_e = 3.80 cm for both telescopes, we can substitute these values into the formula: \[ M = Show more…

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Two refracting telescopes are used to look at craters on the Moon. The objective focal length of both telescopes is $95.0 \mathrm{~cm}$ and the eyepiece focal length of both telescopes is $3.80 \mathrm{~cm}$. The telescopes are identical except for the diameter of the lenses. Telescope A has an objective diameter of $10.0 \mathrm{~cm}$ while the lenses of telescope $\mathrm{B}$ are scaled up by a factor of two, so that its objective diameter is $20.0 \mathrm{~cm} .$ a) What are the angular magnifications of telescopes $A$ and $B$ ? b) Do the images produced by the telescopes have the same brightness? If not, which is brighter and by how much?

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Key Concepts

Angular Magnification

In optical telescopes, angular magnification is defined as the ratio of the focal length of the objective lens to the focal length of the eyepiece. This concept indicates by how much the angular size of the observed object is increased when viewed through the telescope compared to the naked eye, and it is a fundamental parameter in telescope design.

Aperture and Light Gathering Power

The aperture of a telescope, determined by the diameter of its objective lens, is a critical factor in its ability to collect light. The light gathering power is proportional to the area of the aperture, meaning that larger diameters result in more light being collected, which in turn produces a brighter image. This principle is important when comparing the performance of telescopes with different objective sizes.

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