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Ray Tracing Lenses SE - Science gizmo student exploration, answers are included.
Science
High School - Canada
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Name: Kushal Patel Date: 5/7/
Student Exploration: Ray Tracing (Lenses)
Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes.
Vocabulary: concave lens, convex lens, focal point, image, magnification, real image, refraction, virtual image
Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Agnes is trapped on a desert island with nothing but a magnifying glass. She wants to use the glass to focus sunlight and start a fire. She holds the glass above some dry grass as shown at right.
On the diagram, draw the path the Sun rays will likely take from the magnifying glass to the grass.
A magnifying glass is an example of a convex lens —a lens that curves outward on both sides. Why is a convex lens useful for starting fires?
Because the lens can direct the light to a point, it focuses all the light there so that point heats up, and can catch fire.
Gizmo Warm-up The Ray Tracing (Lenses) Gizmo shows light rays passing through a lens. The light rays are bent by refraction as they pass through the lens and form a focused image to the right of the lens.
To begin, turn on the Colorize lines checkbox. Under Show lines , turn off the Central line and the Line through focal point so that only the Parallel line is showing.
- The blue dots in front of and behind the lens are the focal points of the lens. Move the candle on the left back and forth and up and down.
What is always true about the light ray that emerges from the right side of the lens?
It always goes through the focal point.
- Turn off the Parallel line and turn on the Line through focal point. Move the candle. What do you notice
about this line? It is always parallel to the principal axis.
Activity A:
Real and virtual images
Get the Gizmo ready: ● Turn on the Parallel line , Central line , and Line through focal point. ● Move the candle to -24 on the central axis, with the focal point at -12.
Introduction: A convex lens is called a “converging lens” because it focuses light rays into a point. A real image is formed where the light rays emitted from a point converge on the other side of the lens. If you placed a sheet of paper at the image, a focused image would be projected onto the paper.
Question: How do lenses create images?
- Observe: In its current configuration, the distance from the candle to the focal point is 12 units and the distance from the focal point to the lens is also 12 units.
A. What do you notice about the orientation of the candle’s image on the right side of the lens?
It is inverted.
B. What do you notice about the size of the image? The image is slightly smaller.
- Investigate: Complete each action listed in the table below, and describe how that action affects the image to the right of the lens. Return the candle and focal point to their original positions (-24 for the candle, - for the focal point) after each action.
Action Effect on image Move the candle to the left. Image gets smaller and moves toward the lens.
Move the candle to the right. Image gets bigger and moves away from the lens.
Move the left focal point to the left. Image gets bigger and moves away from the lens.
Move the left focal point to the right. Image gets smaller and moves toward the lens.
- Analyze: How is the image size related to the distance between the candle and the focal point?
As the distance between the candle and focal point increases, the image gets smaller and moves towards the lens, and vice versa.
Activity B:
Thin-lens equation
Get the Gizmo ready:
● Select the Convex lens. ● Move the candle to -15 and the focal point to -10. ● Turn off all line segments, and turn on Show ruler.
Question: How is the position of the image related to the position of the object and the focal length of the lens?
- Measure: In this activity, you will measure the relationships between several values:
do : Distance between object and lens
f : Distance between focal points and lens
di : Distance between image and lens
What are the current values of these variables? (Note: If you like, use the ruler to measure di .)
do = 15 f= 10 di = 30
- Gather data: Use the ruler to measure di for each of the following values of do and f. For the last three rows of the table, use your own values of do and f.
do f di
15 10 30 1/15 1/30 1/ 25 10 16 1/25 1/16 1/ 20 10 20 1/20 1/20 1/ 29 10 15 1/29 1/15 1/ 30 15 30 1/30 1/30 1/
- Calculate: Find the reciprocal of each value and fill in the last three columns of the table.
Included in the table above.
- Analyze: For each row of the table, find the sum of and.
1/15 +1/30 = 1/10 1/25 +1/16 = 1/10 1/20 + 1/20 = 1/10 1/30 + 1/30 = 1/
What do you notice? 1/do+ 1/di= 1/f
- Make a rule: Express the relationship between , , and as an equation.
1/do+ 1/di = 1/f
This equation is called the thin lens equation because it assumes a very thin lens. Errors are introduced when a thicker lens is used.
- Practice: A candle is placed 6 cm in front of a convexlens. The image of the candle is focused on a sheet of paper that is exactly 12 cm behind the lens.
What is the focal length of the lens? 4cm
Show your work:
1/do+ 1/di = 1/f 1/6 + 1/12 = 1/f 1/4 = 1/f 4 = f f = 4
- Practice: A candle is placed in front of a convex lens with a focal length of 5 cm. The image of the candle is focused on a sheet of paper that is exactly 15 cm behind the lens.
What is the distance from the candle to the lens? 7
Show your work:
1/do+ 1/di = 1/f 1/do+ 1/15 = 1/ 1/do= 1/5 - 1/ 1/do= 2/ do= 7.
- On your own: Use the Gizmo to determine if the thin-lens equation applies to a concave lens. Report the results of your investigation below. (Hint: If the image is virtual, di and f are negative.)
The thin lens equation does work on the concave lens as they will still give the correct distance for the according variable. However, if the image is virtual in these concave lenses, then you have to make sure that di and f are both negative when placed into the thin lens equation.
Make a rule: The magnification of an image is equal to the ratio of the image height to the object height. Using the ratios from the table on the previous page, write three equations that could be used to calculate magnification:
Practice: A candle is placed 4 cm in front of a convexlens. The image of the candle is focused on a sheet of paper that is exactly 10 cm behind the lens.
What is the magnification of the image? -2.
Show your work:
M = -di / do M = -10/ M = -2.
- Practice: A 29-cm pencil is placed 35 cm in front of a convex lens and illuminated by a spotlight. The focal point of the lens is 28 cm from the lens.
A. What is the height of the pencil’s image? 116cm
B. How far from the lens will the image of the pencil be focused? 140cm
Show your work:
a) hi / ho = f / so hi / 29 = 28/ hi / 29 = 4 hi = 4 x 29 hi = 116
b) hi / ho = di / do 116 / 29 = di / 35 4 = di / 35 4 x 35 = di 140 = di di = 140
- Challenge: When the object is between the focal point and the lens, so is negative. What other values must be negative for your equations to still work? Explain. (Hint: The distance between the focal point and lens ( f ) is never negative unless the lens is concave.)
One other value that has to be negative is di because if the object is between the focal point and the lens, then di also has to be negative because of how it is a VIRTUAL image instead of being a REAL image as it gets refracted to the same side as the object. Due to that explanation, that then means the hi and si also have to be negative as well
Ray Tracing Lenses SE - Science gizmo student exploration, answers are included.
Subject: Science
High School - Canada
• 10
