astronomy labs

Revised - 6/8/2020 The Lens Equation - 1

Laboratory 2

THE LENS EQUATION Purpose To study the central idea of the science of optics, the lens equation. Introduction In astronomy, we observe objects with light since the distances are so large. With the light we must combine the other senses of taste, touch, smell, hearing, and seeing. In order to do this, we must manipulate the light. We do this by allowing the light to enter a denser (i.e. a liquid or solid) object or being bounced off the same object. The two processes are called refraction and reflection, respectively. We use lenses made of glass to refract light and mirrors to reflect light. They both focus light onto one point and obey a single equation called the lens equation. In this lab, we will focus on the convex lens, the optical system that most telescopes use this type of lens or its complimentary system the concave mirror system. The convex lens works like this:

where the object is focus into an image on the other side of the lens. The formula to determine the focal length of the lens is:

DistanceImage 1

DistanceObject 1

LengthFocal 1

+= Equation 1

For optical systems we also want to know about the magnification of the images. We want to see how we can manipulate the different images. We can determine this from the ratio of the object size to the image the lens creates. Or we can determine this from the ratio of the object distance to the image distance at the position of the lens creating that image size. The geometry is as follows:

Distance Object Distance Image

Ratio DistanceionMagnificat Size Object Size Image

=== Equation 2

Object Size

Image Size

Revised - 6/8/2020 The Lens Equation - 2

Procedure

1. Open https://ophysics.com/l12.html. This is the opening screen:

2. Move the focus point show that it shows f = 2 by clicking that focal point. Now make sure the object is size 2 and it is three squares away from the focal point. Record the object distance, image distance, and absolute value of image height in Table 1. Do this for four other object positions.

3. Move the focal point to f =4 and repeat the procedure from step 2.

4. Now complete Table 3 based on the data from Tables 1 and 2.

Revised - 6/8/2020 The Lens Equation - 3

Data Sheet Laboratory 2

Table 1 f = 2, ho = 2 Object Distance

Image Distance

Image Size

1/Object Distance

1/Image Distance

1/ Focal Length

Table 2 f = 4, ho = 2

Object Distance

Image Distance

Image Size

1/Object Distance

1/Image Distance

1/ Focal Length

Table 3 Magnifications and Distance Ratio

f= 2: For the Smallest Image Size: Magnification = Image Size/Object Size = ____/____ = Distance Ratio = I/O = ____/______= For the Largest Image Size: Magnification = Image Size/Object Size = ____/____ = Distance Ratio = I/O = ____/______= f = 4: For the Smallest Image Size: Magnification = Image Size/Object Size = ____/____ = Distance Ratio = I/O = ____/______= For the Largest Image Size: Magnification = Image Size/Object Size = ____/____ = Distance Ratio = I/O = ____/______=

Revised - 6/8/2020 The Lens Equation - 4

Questions

1. Mirrors tend to be lighter than the equivalent lenses. If you were developing a telescope that would need to collect light from a dim source, would you use a lens, multiple lenses, a mirror, or multiple mirrors to build the telescope? Defend your answer using your data and telescope simulators from the internet.

2. Can we use the distance ratios to find the magnifications? Analyze our understanding of lens characterization.

3. Analyze the shape of the lens with respect to focal length.