Object and Image Distances_STUDENT_PHET_ND_edited
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Object and Image Distances Thin Lens_UTRGV Page 1 of 10 Object and Image Distances Thin Lens Equipment PHET Simulation geometric optics Introduction The purpose of this activity is to determine the relationship between object distance and image distance for a thin convex lens. Use a light source, optics bench, lens, and viewing screen to measure object distance, image distance, and image size. Figure 1: Equipment Background The behavior of light through a thin lens is utilized every day in simple devices that we use. Some of these devices include magnifying glasses, telescopes, and binoculars. Even the human eye takes advantage of the lens found in its outer surface, focusing images so we can see clearly.
Object and Image Distances Thin Lens_UTRGV Page 2 of 10 Lenses are common optical devices made of transparent material (glass or plastic), which refract (bend) light. On a small scale, the behavior of light that crosses a boundary between two media, entering a medium 2 from medium 1, can be described using Snell's Law (Figure 2)
: Figure 2. Snell’s Law. sin
i
/ sin
r
= n
2
/ n
1
Here
i
and
r
are the angles of incidence and refraction, respectively; n
1
and
n
2
are the
indexes of refraction for medium 1 and 2, respectively. The index of refraction of a medium
depends on the speed of light inside the medium, and provides a factor by which the speed of
light is reduced in the medium compared to vacuum. Index or refraction of air is approximately
1, meaning that the speed of light in the air is approximately the same as in vacuum. Typically, one or both sides of the lens have a spherical curvature. When parallel light
from a source impinges on a converging lens perpendicular to the plane of the lens, the rays are
refracted so that all the light comes together at a focal point, forming a real image. Another basic type of lens is the diverging lens. With a diverging lens, parallel rays are spread out by the lens. The focus of a diverging lenses is formed by extensions of diverging rays, and is on the same side of the lens as the incident parallel rays (Figure 3). Figure 3: Converging lens (left) and diverging lens (right)
Object and Image Distances Thin Lens_UTRGV Page 3 of 10 An imaginary line drawn through the center of the lens and perpendicular to the lens is
called the principal axis. Converging lenses refract light toward the principal axis, and diverging
lenses – away from it, therefore diverging lenses do not form a real image. Using a more macroscopic scale, the behavior of light can be characterized using spatial
measurements and simple geometry that involves the distance between the object of interest and
the lens, known as "object distance", the distance between the lens and the object image, known
as "image distance", and the distance between the lens’ center and its focal point known as "focal
length" (Figures 4 and 5). Figure 4: Image Formation by a Thin Lens The following equation is known as the thin lens equation that relates the distance of the
object from the lens, d
o
, and the distance of the image from the lens, d
i
, to the focal length of the
lens, f (Figure 5). (1)
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Object and Image Distances Thin Lens_UTRGV Page 4 of 10 Figure 5: Ray diagram for the thin lens equation (O – object, I – image, F- focal point) The lateral magnification produced by a lens is defined as: M = h
i /h
o = - d
i /d
o (2) Since the right triangle formed by the ray through the center of the lens, the object distance and
height is similar to the triangle formed by the ray through the center, the image distance and
height, the ratio of h
i
/ h
o
= - d
i
/d
o
.
The lateral magnification produced by a lens is not constant,
it depends on the properties of the lens (f), position of an object (d
o
), and the resulting d
i
, where
the detector (screen) should be positioned. The following sign conventions are used with the thin-lens and magnification equations (assuming the light source is positioned on the left): •
f is positive (+) for a converging lens; f is negative (-) for a diverging lens. •
d
o
is positive (+) when the object is to the left of the lens (real object); d
o
is negative (-) for an object to the right of the lens (virtual object). •
d
i
is positive (+) for an image formed to the right of the lens for a real object; d
i
is negative (-) for an image formed to the left of the lens (on the same side as the object) for a real object. •
h
i
is positive (+) for an image that is upright with respect to the object, and negative (-) for an image that is inverted with respect to the object •
M is positive (+) for an image that is upright with respect to the object. M is negative (-) for an image that is inverted with respect to the object.
Object and Image Distances Thin Lens_UTRGV Page 5 of 10 The goal of this lab will be to explore the behavior of light and the images it forms as it travels through a thin lens, and collect data that will help determine how image distance is related to both the object distance and focal length of a thin convex lens. Setup
1-
Go to https://phet.colorado.edu/en/simulation/geometric
-
optics
2-
Click on play. 3-
Make sure that Adobe Flash is installed for your browser. 4-
Move the object to see how the image is moving. 5-
Put the object at the focal point of the lens, the image will be at infinity.
Object and Image Distances Thin Lens_UTRGV Page 6 of 10 6-
Move the object closer to the lens (inside the focal point). The image will be virtual, (at the same side from the lens as the object). Click on the virtual image checkbox if you don’t see it. 7-
Set the curvature radius at 0.6 m 8-
Click on the ruler to activate it
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Object and Image Distances Thin Lens_UTRGV Page 7 of 10 Procedure Fill the table. Table I: Object and Image Distances 𝑂𝑏𝑗𝑒𝑐𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 , 𝑑
?
(cm) 𝐼𝑚𝑎𝑔𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 , 𝑑
𝑖
(cm) Magnification, m=
−𝑑
𝑖
𝑑
?
80 200
-2.5
90 154
-1.7
100 132
-1.3
110 118
-1.1
120 108
-0.9
130 102
-0.8
140 96
-0.7
1.
Adjust the object at the distance of 80 cm from the lens using the ruler. (from the tip of the pencil to the center of the lens)
Object and Image Distances Thin Lens_UTRGV Page 8 of 10 2.
Measure the image distance using the ruler.
Object and Image Distances Thin Lens_UTRGV Page 9 of 10 3.
Record the image distance in table 1. (Hint it is about 160 cm). 4.
Calculate the magnification m=
. Magnification should be negative since the image is inverted. 5.
Adjust the position of the object from the lens to the next object distance listed in Table I of 90 cm. 6.
Measure the image distance and record in Table I. 7.
Repeat the same procedure for each object distance value in Table I. Record all values in Table I. 8.
Calculate the magnification for all the object and image distance. Analysis: Distance Make a graph of 1/d
i
vs. 1/d
o 1.
Apply a linear fit to your data and write the y = mx + b equation that describes the line below. 2.
Write the b value which is the y-intercept in your lab report. 3.
What is the significance of the y and x-intercepts in your graph/equation? 4.
Based on your y-intercept (b) calculate the focal point of the lens. (f=1/b) Analysis: Magnification 5.
Create two more graphs: Magnification as a function of object distance and Magnification
as a function of image distance. 6.
How is magnification related to object distance (proportional, inverse, etc.), and at what object distance is the magnification approximately equal to 1 (object height = image height)?
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Object and Image Distances Thin Lens_UTRGV Page 10 of 10 7.
How is magnification related to image distance (proportional, inverse, etc.), and at what image distance is the magnification equal to 1? How does this value compare to the object distance at the same magnification? 8.
Based on the responses to the previous two questions, what is the mathematical relationship that relates magnification to object and image distance? 9.
What value does magnification approach as object distance approaches the focal length of
the lens (100 mm)? What do you think happens to the image when the object distance is less than the focal length of the lens? (Note: The above analysis questions are in the lab report. Put your answers there. )