Using the semi log graph paper, make a hand drawn plot of the transmittance on the vertical axis and the thickness on the horizontal axis. Draw a best fit line through the points, which should generally fall along a straight line with a negative slope.
Using the semi log graph paper, make a hand drawn plot of the transmittance on the vertical axis and the thickness on the horizontal axis. Draw a best fit line through the points, which should generally fall along a straight line with a negative slope.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Using the semi log graph paper, make a hand drawn plot of the transmittance on the vertical axis and the thickness on the horizontal axis. Draw a best fit line through the points, which should generally fall along a straight line with a negative slope. Do not simply connect the adajcent points.
Transcribed Image Text:### Semi-log Graph
**Description:**
A semi-log graph is a way of visualizing data in which either the horizontal or the vertical axis is scaled logarithmically, while the other axis is linear. This type of graph is particularly useful for representing data that changes exponentially, such as growth rates or decay processes.
**Graph Features:**
- **Axes:** The graph consists of two axes — one is linear, and the other is logarithmic. This allows for easy visualization of data across a wide range of values.
- **Grid Structure:** The grid is divided into several logarithmic cycles, each containing ten equal subdivisions. This makes it easier to plot data that spans several orders of magnitude.
This kind of graph is commonly used in scientific fields to analyze data related to population growth, radioactive decay, or acoustic waves, among other applications. It helps in understanding trends that linear graphs might not reveal.
Transcribed Image Text:**Material Thickness and Light Transmittance Analysis**
The table below presents data on the relationship between the thickness of a material (in micrometers) and its corresponding light transmittance. Transmittance values range from 0 to 1, and the logarithmic transformation of transmittance values, specifically Log10(Transmittance), is also provided.
| Material Thickness (µm) | Transmittance (0 to 1) | Log10(Transmittance) |
|-------------------------|------------------------|----------------------|
| 0.166 | 0.830 | -0.0809 |
| 0.275 | 0.770 | -0.114 |
| 0.596 | 0.600 | -0.222 |
| 0.729 | 0.560 | -0.252 |
| 0.869 | 0.510 | -0.292 |
| 1.0 | 0.380 | -0.420 |
| 1.5 | 0.300 | -0.523 |
| 2.0 | 0.190 | -0.721 |
| 2.8 | 0.110 | -0.959 |
| 4.6 | 0.0230 | -1.64 |
| 5.4 | 0.0120 | -1.92 |
**Explanation and Observations:**
1. As the thickness of the material increases, the transmittance decreases. This suggests an inverse relationship between material thickness and light transmittance.
2. The logarithmic values of transmittance help illustrate this relationship. As the transmittance decreases, the negative values of the logarithmic transmittance become larger in magnitude.
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