Questions: Problem 1: (10% of Assignment Value)
Problem Status
A student stands (do=2.5 m) in front of a floor-to-ceiling mirror. Her eyes are (he=1.43 m) above the floor and she holds a flashlight at a distance (hf=0.75 m) above the floor.
Randomized Variables
(do=2.5 m)
(he=1.43 m)
(hf=0.75 m)
Transcript text: Problem 1: ( $\mathbf{1 0 \%}$ of Assignment Value)
Problem Status
A student stands $d_{\mathrm{o}}=2.5 \mathrm{~m}$ in front of a floor-to-ceiling mirror. Her eyes are $h_{\mathrm{e}}=1.43 \mathrm{~m}$ above the floor and she holds a flashlight at a distance $h_{\mathrm{f}}=0.75 \mathrm{~m}$ above the floor.
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Randomized Variables
\[
\begin{array}{l}
d_{\mathrm{o}}=2.5 \mathrm{~m} \\
h_{\mathrm{e}}=1.43 \mathrm{~m} \\
h_{\mathrm{f}}=0.75 \mathrm{~m}
\end{array}
\]
Solution
Solution Steps
Step 1: Understanding the Problem
The problem involves a student standing in front of a mirror, with her eyes and a flashlight at different heights above the floor. We need to determine how these heights and distances relate to the image seen in the mirror.
Step 2: Analyzing the Mirror Reflection
In a plane mirror, the image of an object appears to be the same distance behind the mirror as the object is in front of it. Therefore, the image of the flashlight will appear at the same height above the floor as the flashlight itself, and the same distance behind the mirror as the flashlight is in front of it.
Step 3: Calculating the Image Position
Given:
Distance of the student from the mirror, \( d_{\mathrm{o}} = 2.5 \, \text{m} \)
Height of the flashlight above the floor, \( h_{\mathrm{f}} = 0.75 \, \text{m} \)
The image of the flashlight will appear:
At a height of \( h_{\mathrm{f}} = 0.75 \, \text{m} \) above the floor.
At a distance of \( d_{\mathrm{o}} = 2.5 \, \text{m} \) behind the mirror.
Final Answer
The image of the flashlight appears at a height of \( \boxed{0.75 \, \text{m}} \) above the floor and \( \boxed{2.5 \, \text{m}} \) behind the mirror.