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Chapter 4: Problem 10

Suppose that we use a reflector in the coudé focus, and each of the three mirrors reflects \(95 \%\) of the light. What fraction of the light is lost as a result of these three reflections?

Short Answer

Expert verified
Results in a loss of 4.7% of light over 3 mirrors reflecting 95% each.

Step by step solution

01

- Understand the problem

The problem involves calculating the fraction of light lost after reflecting off three mirrors, each reflecting 95% of the light. You'll need to determine what fraction of light is reflected after each mirror and then calculate the total fraction of light lost after three reflections.
02

- Calculate light reflected by one mirror

One mirror reflects 95% of the light. This means it loses 5% of the light because
03

- Calculate the total light reflected by three mirrors

The total fraction of light reflected by three mirrors is
04

- Calculate light lost by three mirrors

Given that each mirror reflects 95% of the light, find the total light lost by calculating
05

- Calculate the final fraction of light lost

The final fraction of light lost is calculated by taking

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Coudé Focus
In telescopes, the coudé focus is a particular point where light is redirected after reflection. This focus is achieved when light is bounced off several mirrors, directing it to a fixed location away from the telescope's main structure.

This setup is useful for attaching heavy instruments that cannot be mounted directly on the telescope. Engineers and astronomers use the coudé focus to perform detailed analyses or take high-precision measurements without destabilizing the system.

By steering light through multiple reflections, the coudé setup ensures that all light converges at one convenient point, making observations and data collection more efficient.
Reflector Telescope
A reflector telescope uses mirrors rather than lenses to gather and focus light. The primary advantage of this type of telescope is its ability to capture more light while minimizing optical aberrations.

Key components of a reflector telescope include:
  • Primary Mirror: Captures incoming light and reflects it to a focal point.
  • Secondary Mirror: Redirects the light, often to an eyepiece or detector.
Reflector telescopes come in various designs, such as Newtonian, Cassegrain, and Gregorian.

Each design offers different advantages, such as reduced size, cost, or ease of use. Reflectors are favored in both amateur and professional astronomy for their powerful performance and versatility.
Light Loss Calculation
When light reflects off surfaces, a fraction is inevitably lost. This loss is expressed as a percentage.

In the given problem, each of the three mirrors reflects 95% of the light, which means each mirror loses 5% of the light.

The steps to calculate the total light loss are as follows:
  • Calculate the light reflected by one mirror: \(0.95 \times \text{incoming light}\)
  • Determine the total light reflected after three mirrors: \(0.95^3 \)
  • Calculate the light lost: \(1 - 0.95^3 \)
Mathematically, the calculation looks like this:

The reflected light after one mirror is: \(0.95\)
After two mirrors: \(0.95^2 = 0.9025\)
After three mirrors: \(0.95^3 = 0.857375\)

The fraction of light lost is: \[1 - 0.857375 = 0.142625\]

Therefore, the total light loss is approximately 14.26%.

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Most popular questions from this chapter

Generally CCDs have fewer picture elements (pixels) than do photographic plates, so if you want to image a large field, a single photograph might suffice, but you would need a number of CCD images. Suppose you had to make a \(3 \times 3\) square of \(\mathrm{CCD}\) images to cover your single photographic field, and that your photograph has a quantum efficiency of \(5 \%\) while your CCD has an efficiency of \(80 \%\). How long will the needed CCD images take relative to the time for the photograph?

A diffraction grating has \(N\) lines, a separation \(d\) apart. The spectrum is projected on a screen a distance \(D(\gg d)\) from the grating. Two lines are \(\lambda\) and \(\lambda+\Delta \lambda\) apart. How far apart are they on the screen?

Two infrared sources in the Orion Nebula are 500 pc from us and are separated by 0.1 pc. How large a telescope would you need to distinguish the sources at a wavelength of \(100 \mu \mathrm{m} ?\)

How many pairs of telescopes are there in (a) the VLA with 27 telescopes, (b) the VLBI, with ten telescopes, (c) the proposed Millimeter Array, which may have 40 or 75 telescopes depending on the final design?

Suppose we are observing an infrared source that is 500 pc away. It radiates like a \(50 \mathrm{K}\) blackbody and is 1 pc in extent. (a) What is the total energy per second per square meter reaching the Earth from this source? How does that compare with the total amount of solar radiation reaching the Earth per second per square meter. (b) Suppose we observe this source using a satellite with a \(1 \mathrm{m}\) diameter mirror, and we observe at a wavelength of \(100 \mu \mathrm{m} .\) What is the energy/s/Hz striking the telescope? (c) Suppose the telescope radiates like a blackbody at \(300 \mathrm{K}\), but with an efficiency of \(1 \% .\) (That is, the spectrum looks like that of a blackbody but with an intensity reduced by a factor of \(100 .\). What is the energy/Hz/s given off by the telescope at this wavelength? How does your answer compare with that in (b). (d) Redo part (c), assuming that we can cool the mirror to \(30 \mathrm{K}\) (still with a \(1 \%\) emission efficiency
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