# See The Light

 Author: David Macmorine Unit Title: See The Light Grade: 10-12  Subject: Algebra II, PreCalculus Estimated Duration: 2 Weeks Unit Activities: Activity 1: Measuring Luminosity Activity 2: Reflection and Refraction Activity 3: Design of Solar Tube Background Knowledge:  Teachers should know the Inverse Square Law as it relates to illumination. Teachers should familiarize themselves with how to measure light either with a light meter or a light meter app.  Many apps are available free. Date: July 2014
##### The Big Idea (including global relevance)

Electricity used for lighting consumes about 17% of the total electric costs in the United States (http://www.eia.gov/tools/faqs/faq.cfm?id=99&t=3).  Fluorescent compact bulbs are replacing incandescent bulbs, but the fluorescent bulbs are more difficult to dispose of properly.  Sunlight is free.  Natural light has health benefits (http://www.archlighting.com/daylighting/the-benefits-of-natural-light_o.aspx).  But what if you have an interior room with no windows and no way to install a skylight.  How can we ‘channel’ exterior light to one of these interior rooms? (see http://en.wikipedia.org/wiki/Light_tube).

##### The Essential Question

How can we easily and cheaply direct sunlight into a closed interior room?

##### Justification for Selection of Content

The mathematics of light can be linked across the curriculum from geometry (angles of reflection and refraction) to calculus.  Students will learn to compute the luminosity of light from concepts of aperture and exposure time involving fractions, and film speed from chemistry.  The particle/wave duality of light is a topic of physics, whereas the inverse square law is directly applied in lighting applications from home to the stage.  The measurement of light (lumens) is a necessary skill for the study of light.

##### The Challenge

Students will build a solar tube to transmit sunlight 3 feet with a least two bends of 30 degrees or more.

##### The Hook

Do you like being outside in the sunshine?  Do you like the warm sun on your face?  Don’t you hate having to be inside working on a nice sunny day, especially when you are stuck inside in a room with no windows?  Under fluorescent light? Wouldn’t a little bit of sunshine be nice?

##### Teacher's Guiding Questions
• What is light?
• How does electricity produce light?
• How does the sun produce light?
• How do we measure light?
• What methods do we have to light up the inside of a building?
• Can technology duplicate sunlight?
• Are their health benefits of sunlight?
• Do different cultures prefer different kinds of artificial light?
• Are there different types of windows?
• How do windows let light in?

• Is a lot of sunlight ‘wasted’?
• How do we get sunlight inside a building?
• What happens if you are in a room with no windows and no skylight?
• Is there any way of getting sunlight into a room like that?
##### ACS (Real world applications; career connections; societal impact)

Applications -   Solar tubes exist, and are available to purchase at hardware stores. There are several designs which civil engineers and architects can use.   Some laws mandate natural light (http://en.wikipedia.org/wiki/Right_to_light).

Careers - Natural light and lighting must be taken into account in architecture, theatrical lighting, optics, and physics. Civil engineers and architects must also be familiar with the mathematics of light and optics.  Environmental engineers are working on systems to bring sunlight to interior rooms.

Societal Impact – Natural light is desirable.  It is free, and has health benefits.

##### Engineering Design Process (EDP)

Students will be presented with the challenge of funneling light from a source, through a device which must make at least two 30 degree turns and extends a distance of 3 feet.  The students must measure the amount of light of the source (in lumens) and the amount of light coming through the device and not lose more than 10%.  The light source is initially directly placed at the opening of the tube.  Students must show the computation of the amount of light of the source and coming out of the device and show a loss of less than 10%.  If the loss of light is greater than 10%, students must revisit their design and make improvements to achieve a loss less than 10%.  For redesign, the light source will be moved 1 foot away from the tube opening so students will have to design a light ‘collector’ to direct the light down the tube.  If the loss of light from the solar ‘collector’ is greater than 10%, the students must redesign again to have a light loss less than 10%.

##### Unit Academic Standard

HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media.

1-PS4-2. Make observations to construct an evidence-based account that objects can be seen only when illuminated.

1-PS4-3. Plan and conduct an investigation to determine the effect of placing objects made with different materials in the path of a beam of light.

##### Unit Activities

Activity 1 Measuring Luminosity

• Worksheet on luminosity calculations
• Worksheet on the Inverse Square Law

Activity 2 Reflection and Refraction

• Worksheet on Refraction
• Worksheet on Reflection

Activity 3 for design of Solar Tube

• Worksheet for Design of Solar Tube
• Worksheet for Testing Solar Tube

Activity 1

##### Background Knowledge

Teachers should know the Inverse Square Law as it relates to illumination.  Teachers should familiarize themselves with how to measure light either with a light meter or a light meter app.  Many apps are available free.

##### Misconceptions

The growth of digital photography has made the taking and sharing of photos extremely easy.  The mathematics behind photography remains the same regardless.  By studying concepts of photography, students will gain an appreciation of what they may have been taken for granted.

http://www.exploratorium.edu/snacks/inverse_square_law/index.html

##### Results: Evidence of Growth in Student Learning

Post test scores increased 38% from pre test scores.

##### Reflection

The unit was quite successful. Students were interested in the mathematics of photography and how measuring light is used for the artistic nature of taking pictures.  Designing a device to transmit light was, as one student said, ‘easy to state, but hard to do.”.

Post test scores increased 38% from pre test scores.