Optical Powers
Focal Length

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Activity 5b Experimenting with Focal Length

An Analogy:

Imagine sets of funnels, each set having the same diameter but differing in length of the cone. We have seen that telescopes with larger openings or apertures gather more light. But how else are telescopes like or different from funnels? 

We know that the cone shape of the funnel directs liquids into a container. Light however cannot be slid down a ramp, blown by a fan or flow down a funnel.  Telescopes direct light by changing the direction the light is traveling.  Light can be reflected off a curved mirror or bent as it passes through a lens. Light that is reflected or bent comes into focus some distance from the collecting mirror or lens.  One might think of the bottom of the cone of the funnel as the focal plane, and the container as the detector measuring the amount of light.

The distance between the lens or mirror and the place where the light comes into focus is called the focal length. If all telescopes gather light and bring it into focus, why do astronomers care about the focal length of the telescope?


Geometry of similar triangles and ratios are important mathematical skills related to analyzing images to find the effects of focal length.  For homework, construct similar triangles, then measure and compare ratios of similar sides. 


What effect does focal length have on the image we receive from a telescope? 

The Experiment:

Conducting an experiment to address this question is a bit tricky.  Because the focal length is a property of the how much the lens or mirror is curved, once a telescope is constructed, it is not possible to simply change its focal length in a simple way like we used a mask to change the aperture.  Changing the focal length can be accomplished with extra lenses in the light path; however this is expensive and can introduce other anomalies such as internal reflections of bright stars.  This is one of the reasons people take such care in choosing telescopes. 

The image sets compare images taken on telescopes with different focal lengths.  But other factors are not controlled in all cases.  The aperture of the telescope, the exposure time, etc. are varied.  If you are not sure if aperture affects image size, or if exposure time affects image size, you should go back to previous activities to investigate.




Procedure:  Using HOU software, you will compare images sets taken with  telescopes having different focal lengths.  You will make observations and gather data about image size.  Then use the slice tool to measure the distances on both images between the same features.  Look up the focal length of each telescope in the image info or in the paragraph that follows about the image sets.  Compare the ratio of the focal lengths of the telescopes to the ratio of the measurements between the two stars or the same features on the respective images.   Create a data table and/or spread sheet and graph to show your results.  The images in each set were each taken with the same CCD.  Study how much of the object can be seen in the entire image.  Consider the effect focal length has on the field of view. 

Image Sets:

Compare the images in one or more of these sets to determine the effect differences in focal length have on the image.

Image sets Information
Images: m42_st7_160cm_gh10in.fts, m42_st7_250cm_km10in.fts

Orion Nebula, M42. This set compares two Meade LX200, 10 inch telescopes, with different focal lengths.  The f/6.3 has 160 cm focal length and the f/10 has a 250 cm focal length.  These images were taken using an SBIG ST7 CCD, both binned 2x2, yielding 18 micron pixels. (Binning combines pixels. Originally the pixels are 9 microns. Binned across and down to be double in size creates 18 micron pixels.)

Images: m42_ap7p_305cm_fm12in.fts, m42_ap7p_824cm_y24.fts

Orion Nebula, M42.  The second set compares a Meade LX200, 12 inch, f/10 telescope with the Yerkes 24 inch, f/13.5 telescope.  The respective focal lengths are 305 cm and 823 cm. Both images were taken with the Apogee AP7p CCD with 24 micron pixels.

Images: The two M57 images.

Ring Nebula, M57.  This set compares a Meade LX200, 8 inch, f/6.3 telescope with the Yerkes 24 inch f/13.5 telescope, using an Apogee AP7p CCD with 24 micron pixels. Focal lengths are 128 cm and 823 cm respectively.

Images: The two Saturn images

Saturn. These images of Saturn were taken during the same week in November of 1999.  One image was taken with a Meade 10 inch f/10 telescope.  The other images was taken with the Yerkes 24 inch f/13.5.   Both images were taken with the SBIG ST7 CCD, both binned 2z2, yielding 18 micron pixels.  Focal Lengths are 250 cm and 824 cm respectively.  

Note: When comparing image size using solar system objects, it is important to also consider the date of the observations.  These images of Saturn were taken the same week, so that the angular size is nearly the same.    Because of the changing positions of the Earth and all other solar system objects due to revolution around the Sun, angular size of objects changes because the relative distance between the objects and the Earth changes.  Angular size is constant because the Saturn images were taken in the same time frame.

Note on Focal Lengths for the Meade Telescopes
Focal lengths of Meade telescopes in metric units are listed as described in the Meade telescope manual. The values differ slightly from what would be expected based on conversion from inches to metric.  1 inch = 2.54 cm.  So one would expect a 10 inch telescope with an f/10 focal ratio to have a focal length of 254 cm, not 250 cm, as listed in the catalog. Apparently some information is approximate, with the inches measurement listed to the nearest inch.

Analyze the Images and Record Data:

Gather the data needed to answer the problem.  Record your observations, measurements and analyses.  Consider using a spreadsheet and graphing tools to organize and present your results.

1.      Select an image set to analyze. 

2.      The images in each set were taken with telescopes of different focal lengths.  The focal lengths are in the image name, and in the chart above.  You can also look in Image Info to find the information about the telescopes. 

3.      With both images open, study the images to find the same features in both.  Then use the slice tool (Data Tools, Slice) to measure between the features. Measuring across the images with slice is a way to compare image sizes.

4.      Make a table to record your data.  Consider entering your data in a spreadsheet and graphing program. 

For each set of images, record:  

Then compute the:

5.      Compare the ratio of focal lengths to the ratio of slices.



6.      Can you predict the ratio of either the slices or the focal lengths if you know one or the other?



7.      Repeat your procedures with the one of the remaining image sets.


Conclusions:  Look carefully at your results.  Use complete sentences to describe:

a)      What happens when we image the same object with telescopes of different focal lengths. 


b)      Does the image size change and if so, how?


c)      Does the field of view change and how?


d)      If we controlled for aperture and exposure time, what do you think would be the effect on brightness when we changed focal lengths?


e)      What new questions do you have?  How could you create experiments to test these questions?


Further Test Your Skills:

Open the images of M15 taken with two 40 inch telescopes at The University of Chicago Yerkes Observatory.. 

One image of M15 was taken with the Yerkes 40 inch refractor at f/19.  The other was taken with Yerkes 40 inch reflector, at f/?.  By comparing image size,  you should be able to determine the f/ratio of the 40 inch reflector when configured for the image taken of M15.

Hint:  F/ratio.  The ratio is computed as focal length divided by aperture.

  1. The University of Chicago Yerkes Observatory Great Refractor has an aperture of 40 inches and a focal ratio of f/19. What is its focal length?

   To answer this question you multiply the aperture by the 19. 

   Focal Length of Yerkes 40 inch refractor is ________________.

  1. What was the f/ratio of the Yerkes 40 inch reflector?  Describe your method and record your data and calculations? 

    The Yerkes 40 inch reflector (nicknamed Yerkes 41 inch so as not to confuse it with the refractor) has two secondary mirrors.  One creates a focal ratio of f/8.  The other a focal ratio of f/13.5. 

    Estimate the f/ratio of the Yerkes 40 inch reflector by comparing image size with the Yerkes 40 inch refractor.  You should be able to study the images and find the same stars in each to measure between using the slice tool. Then work out the numbers to come up with the f/ratio.