Optical Powers
Focal Length

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Activity 5b Experimenting with Focal Length

Standards (see Appendix A):

Unifying Concept:  Systems, Form and Function.

Objective:  

Using HOU-IP image processing software, students compare images sets taken with two telescopes having different focal lengths.  They make observations and gather data about image size. Students compare the ratio of the focal length of the telescopes to the ratio of measurement between the two stars or the same features on the respective images.  The ratios are theoretically the same and nearly the same when using real data.  Students will be able to discover that image size is directly proportional to focal length and that increasing image size decreases field of view, given the same size detector.

Overview:

This activity is designed to help students understand how focal length affects images.  Students will investigate to see how focal length affects image size.  To investigate how brightness and resolution might change with focal length, the variables which should be controlled are: aperture, filters, and exposure time, seeing conditions, focus of telescope, pixel size on the CCD imager.  Since so many variables are difficult to control, the activity is limited to image sets where focal length is the only variable considered as it applies to image size.  Students will be able to discover that:

1.      Image size is directly proportional to focal length.

2.      Increasing image size decreases field of view, given the same size detector.

Other conclusions which could be drawn with better image sets are that:

3.      The brightness of images decreases with focal length.

4.      Focal length does not improve resolution.  

One often can see better detail from telescopes with long focal lengths if there is also a large mirror or lens for gathering light.  In this case, though the image size is large, there is also more light collected per area of the image because the telescope has a large aperture.   (Department store telescopes often boast of high magnification (image size) at the expense of aperture and quality lenses.  High magnification without significant light gathering does not improve image quality.)

Preparation:

Image Sets

  1. There are two sets of the Orion Nebula, M42.  The first 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 for 18 micron pixels. 
  2. The second set of M42 images compares a Meade LX200, 12 inch, f/10 telescope, with the Yerkes 24 inch telescope, f/13.5. Focal lengths are 305 cm and 823 cm respectively.
  3. The Ring Nebula, M57, images were taken with a 10 inch F/10 telescope and the Yerkes 24 inch F/13.5 telescope, using an Apogee AP7p CCD. Focal lengths are 250 cm and 823 cm respectively.
  4. The Saturn images were taken with a Meade 10 inch F/10 telescope and the Yerkes 24 inch F/13.5 the using an SBIG ST7 CCD.  Focal Lengths are 250 cm and 823 cm respectively. Because of the changing positions of the Earth and all other solar system objects due to revolution around the Sun, angular size of these objects change.  The relative distance between the objects and the Earth is the cause.  Angular size is not a factor in comparing these Saturn images, because they were taken at the same time. 

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.

Data Tables or Excel Spread Sheets as designed by teachers or students.

Time:  45 minutes or one class period.

Homework:

See student homework pages providing geometry practice, measurement of similar sides on similar triangles, and comparison of ratios of these measured sides.   This is to help students relate the measurements they make on images to the telescope systems with different focal lengths. 

Data Analysis:

Students will record slice measurements and determine ratios for one set of images, comparing the ratios of focal lengths to the ratios of slice measurements.  In the another set of images, students predict the ratio of slices based on the ratio of focal lengths.  Students also compare the amount of sky, field of view, seen in the images. 

Evaluation:

 Open the images of M15.  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/?  For this last image set, students will estimate the F/ratio of the Yerkes 40 inch reflector based on image size.