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Activity 4a F Box Explorations

Standards (see Appendix A):

• Science Content Standards: A. Science as Inquiry, D. Earth and Space, E. Science and Technology, History and Nature of Science.
• Mathematics Standards: Representation, Measurement, Connections.
• Technology Tools: Productivity; Problem Solving and Decision Making.

Unifying Concepts:  Form and Function; Size and Scale; Evidence, Models and Explanations.

Objective:

Two important characteristics of a telescope are its aperture and focal length.  Students will learn the correct use of these terms and will begin developing an understanding of how they affect qualities of brightness and image size. (magnification):

• Image size is dependent upon focal length
• Brightness is directly dependent upon aperture and inversely dependent on focal length.
• Focal ratio is the mathematical description of the relationship between focal length and aperture. ( f/ratio = focal length/aperture).  Use the f/ratio to find the focal length.  (Multiply the focal ratio by the aperture to derive the focal length.)
• Determine which size pixels are more appropriate for the various focal lengths.  Each image screen has two sizes of graph paper.  Determine which size graph paper is needed to best resolve detail of the projected F image.

Overview:

In this activity, students begin to explore the characteristics of lenses and construct an understanding of how the characteristics of aperture and focal length affect the images we receive from the telescope.  Using a light box and projected letter “F,” students explore how light behaves when it passes through several different lenses.  This activity is set up so that students are exploring lens characteristics independent of the telescope and provides an important foundation for the activities to follow.  Through their exploration, students are introduced to the vocabulary of lenses such as aperture, focal length, focal point and refraction.

Background:

The following exercises explore the properties of telescope images using simple lenses.  Lenses form images by bending light from an object.  The bending of light as it passes through a lens is called refraction. Mirrors are also used in telescopes to produce images.  Mirrors form images by reflecting light.  Much of what you learn about the behavior of light using lenses can be carried over to the study of image formation by mirrors. We will not be discussing mirrors in this activity.

Refraction.  One of the properties of light is that it can be refracted, that means that beams of light can be bent.  You have seen this bending effect if you have ever put fishing pole or a stick into water.  The stick or fishing pole appears to be bent at the surface of the water.  Try this with a pencil in a glass of water.  The refraction or the bending is caused because the light changes speed as it moves between the water and the air. 

We use this refraction as a way of forming images in various optical instruments such as cameras and telescopes.   When light passes though a flat piece of glass at an angle, the light rays are bent as they enter and leave the glass; when they exit the glass they travel parallel to the original beams.  When light passes through a lens that is thinner in the center than the outer edges, a concave lens, the light rays will diverge or move apart. When light passes though a lens that is thicker in the middle than the outer edges, a convex lens, the light rays are brought together at a point.

Focal Point is the point where central parallel light rays (light coming from a very distant source) come together (converge) after passing through a lens or being reflected by a curved mirror..

Focal Plane is the image plane where all the light rays from all the aspects of the original distant source come together after passing through a lens or being reflected by a curved mirror to form an image.

Focal Length is the distance between the center of the lens or curved mirror and the focal point (where the light rays come together.) Focal length is important in telescopes for several reasons.  First, it determines where the eyepiece must be placed in order to see the image.  Second, the focal length determines the size of the field of view.  The longer the focal length of the telescope, the smaller the field of view.  The shorter the focal length the larger the field of view. Third, the focal length determines the image size or magnification.  The longer the focal length the greater the magnification. The shorter the focal length the lower the magnification.  The curvature, thickness and type of glass, determine the focal length of the lens. Thicker lenses have shorter focal lengths.  Likewise, thinner lenses have longer focal lengths.   

Aperture  - Aperture refers to the size of the primary or objective lens (or mirror).  Aperture size is normally expressed as the diameter in naming a telescope. For example: an 8 inch reflector, describes a reflecting telescope with an 8 inch diameter mirror.   

Image size – The physical size of the image on the detector.  The image size is related to how much an image is magnified by a lens or mirror.

Field of view – Angular measure of the sky seen by an observer at the eyepiece or captured by a camera.

Object distance – Distance from the object (light source) to the center of the lens.

Image distance – Distance from image to the center of the lens.  Image distance is equal to the focal length of the lens when the object is at infinity.  Even though the letter “F” in this activity is not infinitely far from the lenses, we can still compare the relative measures for the focal lengths of the three lenses using image distance.

Web Resource:

• Set up the F box so that the projector is 5 meters from the lens array. This is the object distance for this activity. (5 meters is an approximate distance depending on your classroom and the lenses; one meter may work better.  Ideally the light source is at infinity, but this is not practical for the classroom use of this setup.)
• Collect a variety of lenses to use during the lab or for evaluation.. 

1. Distribute the Student Worksheet 1.  Use the directions on the worksheet to guide the group through filling in the chart.  Encourage the use of the new vocabulary as they gather data.

2. Allow individuals or groups time to write conclusions from what they observe.  Some possible conclusions include:
1. The diameter of the lens has no effect on focal length. 
2. The less curved a lens is the longer its focal length will be.
3. The most curved or thickest lenses produce the smallest images and brightest images. 
4. The longer the focal length, the larger the image size, and fainter the image.
5. Images produced by lenses are oriented upside down and backward. Orientation is not affected by focal length.
3. With the index cards and holders at the focal point for each lens, place the masks, one at a time, over the lenses. Before you begin, ask students to make a prediction about what they think might happen.
4. Allow students time to draw conclusions from what they observe:
1. Aperture does not affect image size.
2. Aperture does not affect image orientation.
3. Aperture size does affect the brightness of the image.  The smaller the aperture the dimmer the image becomes. 
4. The same mask on the longer focal length lenses produce the dimmest image. Note:  This illustrates one of the fundamental problems with telescopes.  Increasing magnification or image size is not always a good thing since the image can quickly become so dim that it seriously affects your ability to resolve details.

Lens	Mask	Image Brightness comparing masked and unmasked	Image Distance	Image Size	Image Orientation
A	Masked	Dim   3	88.3 cm	1.65 cm	Upside down and backward
	Unmasked	Bright   3	88.3 cm	1.65 cm	Upside down and backward
B	Masked	Dim  2	55.8 cm	1.12 cm	Upside down and backward
	Unmasked	Bright  2	55.8 cm	1.12 cm	Upside down and backward
C	Masked	Dim  2	18.4 cm	0.37 cm	Upside down and backward
	Unmasked	Bright  2	18.4 cm	0.37 cm	Upside down and backward

Evaluation/Assessment:

Individual students are given a lens that they secure in an upright position using a piece of clay, Styrofoam cup or other device.  Students measure the aperture, determine the focal length, and calculate the f-ratio.  Exchanging data with another student, he/she should be able to write statements comparing the two lenses in terms of the images they produce:

• Which lens will produce the image with the largest image size?
• Which lens will produce the brightest image?
• Each student should calculate the f/ratio for their lens.  Individuals from each team check each other’s work; then teams recheck the work of another team.
• Given any two lenses, students should be able to determine which has the larger aperture without making any measurements.