Aperture Science

Introduction

In optics, an aperture is a barrier or limitation that reduces the amount of light hitting a lens or mirror and consequently makes the image clearer. Apertures are used in cameras, telescopes and even the human eye. Students will “see” these concepts more clearly as you demonstrate the properties of apertures.

Concepts

• Apertures
• Aberrations
• Converging versus diverging mirrors
• Real images versus virtual images

Materials

Safety Precautions

The materials used in this activity are considered safe. Follow all laboratory safety guidelines.

Disposal

All materials may be saved and stored for future use.

Prelab Preparation

1. Obtain the lamp. It must have a shade to shield the lightbulb—that is, it must be capable of directing light as a beam, rather than filling the room. Suggestions include a desk lamp or flashlight.
2. Using permanent marker, draw a large, bold “F” on the lightbulb. Optional: Draw the “F” on an acetate sheet. Then simply tape the acetate sheet over the lamp.
3. Using scissors, create apertures from the black cards using the patterns. Note that each pattern is for six specific f-stop numbers, but any f-stop number may be created using Equation 1 in the Discussion section.

4. Dim the lights in the classroom and cover the windows, if necessary.

Procedure

1. Obtain the mirror support and place the mirror in it by bending the holding prongs wide enough to securely clasp the mirror.
2. Use either a support stand and clamp to hold the mirror support or use a meter stick and meter stick supports to prop up the holder (see Figures 1 and 2).
3. Set up the lamp within a few feet of the mirror, and angle the lamp and mirror in such a way that the image of the letter “F” is projected on the wall.
   {12029_Procedure_Figure_2}
4. Dim the lights and turn on the lamp. Adjust the position of the lamp and mirror so the image is projected on the wall and slightly out of focus. Note: The more out of focus, the clearer the distinction can be made when apertures are used to clarify the image. If the image is too out of focus, however, it will not be clear even with the aperture stops.
5. Have the class note the clarity of the image and record their observations. Note also (if possible) how the image is oriented on the wall (e.g., upright or inverted.)
6. Obtain the six apertures. Place the first aperture in front of the mirror, either by holding it in place or securing it with a bit of poster putty.
7. Instruct students to record any changes in the projected image on the worksheet.
8. Repeat steps 6 and 7 with successive apertures. Note: As the hole gets smaller, the image gets clearer, but at a price—it also gets dimmer.

Student Worksheet PDF

12029_Student1.pdf

Teacher Tips

• This kit may be performed an indefinite number of times; all materials are reuseable.
• Teach your students to make an aperture anywhere to see far away objects more clearly. Using your thumb and first two fingers, create a small triangle using thumb as the base of the triangle, and your pointer and middle finger as the two vertices. Distant fuzzy objects can often be made clearer by viewing them through this tiny aperture.
• This lab may also be used to discuss the difference between “real” and “virtual” images. Switch the mirror so the convex side is faced toward the lamp. No image will be visible, as the image formed in the mirror is virtual, and the reflected rays will not converge.
• For further investigation of optics, consider the Meter Sticks Optics Bench Kit, Flinn Catalog No. AP6098, and the Optics Kit, Flinn Catalog No. AP9042.

Sample Data

Answers to Questions

1. Based on your observations, what can you conclude about the relationship between aperture size, f-stop number, and the sharpness of the image?

   As aperture size decreases, the f-stop number increases, and the sharpness of the image increases.

2. Given that the diameter of the mirror used in this demonstration is 7.5 cm, and its focal length is 20 cm, it can be considered an aperture itself. Why? What would be its f-stop number?

   Because the diameter of the mirror is smaller than the focal length, the amount of light that hits the mirror is limited by its border. The f-stop number can be found using Equation 1:

   {12029_Discussion_Equation_1}

   where D = 7.5, f = 20, giving an f/# of 2.6.

3. What are the advantages and disadvantages of using an aperture?

   Using an aperture results in a sharper image, but the amount of light is sacrificed. This results in an image that is dimmer. Depending on the application, it might be more valuable to have a sharp image than a bright one, meaning that a smaller aperture would be appropriate. However, some applications require more brightness, so either a larger aperture or no aperture should be used.

Discussion

An aperture is an opening that restricts the amount of light striking a lens or mirror. This may be done by putting a barrier with a hole in front of the lens. Alternatively, the barrier may be the size of the mirror itself when compared with its focal length. Limiting the amount of light generally increases the clarity of an image. For one, it results in more collimated light. Collimated light essentially means the wave fronts are uniform and even instead of random. Narrowing the opening through which light passes before striking a mirror or lens will result in only the more collimated light making it through (see Figure 3). Additionally, mirrors and lenses all have natural defects known as aberrations. These cause light to reflect more randomly, instead of through the focal point, which interferes with the image. For the same reason as with incoming light, the more scattered reflections or refractions of the outgoing light will likely get filtered out by not making it through the small barrier. Of course, the clarity obtained using an aperture comes at a price—limiting the light and reducing the intensity results in a dimmer image.

Aperture size is calculated using Equation 1.

where

Apertures are referred to by their f-stop number, typically in increments of powers of the square root of two—that is:

Each step is referred to as a full stop, and indicates that half of the amount of light is let in. The amount of light allowed through the aperture is proportional to the area. As the area of a circle is πr², the area of the aperture is given by Equation 2.

It can be seen from this equation that increasing the f-stop number by the square root of 2 will decrease the area by a factor of two, reducing the intensity of the incoming light by one-half.

In photography, different apertures are used for many reasons. In addition to clarifying images, apertures limit the amount of light exposure the film receives, allowing a photographer to use a higher or lower shutter speed with the correct aperture size without overexposing the film. A low shutter speed would require a small aperture, and allows for pictures that can be sharp in both the foreground and the background. A higher shutter speed can have a larger aperture, creating pictures that are sharp only at the right focal length. The aperture size is controlled by an adjustable diaphragm. The aperture in telescopes is not a deliberate barrier, but instead generally refers to the diameter of the main objective mirror (for reflecting telescopes) or lens (for refracting telescopes). For example, the mirror in this demonstration is itself an aperture, as its diameter is smaller than its focal length. With telescopes, larger telescopes generally mean larger apertures. This allows more light to be collected from distant galaxies and stars. A large aperture will not be needed on a telescope for viewing the moon and many of the objects within the solar system, such as the planets, as these reflect a great deal of the light from the sun. But the dim light of distant galaxies and nebula and other deep space objects require as much light as possible to be gathered in order for us to view them. Since the mirror in a telescope must be of such high quality, larger mirrors are far more expensive, which forces a practical balance between aperture diameter and cost. The pupil of the eye is also an aperture. In bright lighting, it narrows to limit the amount of light coming to the eye. In dim lighting, the pupil dilates (increases in size) to allow more light to enter.

References

Bilash, B. & Maiullo, D. A Demo a Day—A Year of Physics Demonstrations; Flinn Scientific: Batavia, IL, 2009; pp 329–30.

Hecht, E. Optics 4th ed. Addison Wesley: Reading, MA, 2001; pp 116–20.