Question

psc20 - curved mirror drawings and calculations
name: xavia

1. concave mirror → variables: f = 5.0 cm d_o = 11.0 cm h_o = 2.0 cm

*use a compass when drawing your mirror!
drawing (measure everything in cm and estimate to 2 decimal places)
characteristics of image: ____, __, ____ d_i = ______ h_i = ______
calculations (use the initial variables to calculate the h_i & d_i). **all calculations to 2 decimal places
image distance calculation\timage height calculation
percentage error = \left|\frac{calculated - measured}{calculated}\
ight| x 100%
percentage error for image distance\tpercentage error for image height
***need percentage error that is ≤ 10%.

Explanation:

Step1: Recall Mirror Formula

The mirror formula is $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$, where $f$ is the focal length, $d_o$ is the object distance, and $d_i$ is the image distance. Given $f = 5.0\ \text{cm}$ and $d_o = 11.0\ \text{cm}$, we solve for $d_i$.

First, rearrange the formula: $\frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o}$

Substitute the values: $\frac{1}{d_i} = \frac{1}{5.0} - \frac{1}{11.0} = \frac{11 - 5}{55} = \frac{6}{55}$

Then, $d_i = \frac{55}{6} \approx 9.17\ \text{cm}$ (to 2 decimal places)

Step2: Recall Magnification Formula

The magnification formula is $m = -\frac{d_i}{d_o} = \frac{h_i}{h_o}$, where $h_i$ is the image height and $h_o$ is the object height. Given $h_o = 2.0\ \text{cm}$, we solve for $h_i$.

First, calculate magnification: $m = -\frac{9.17}{11.0} \approx -0.83$

Then, $h_i = m \times h_o = -0.83 \times 2.0 \approx -1.66\ \text{cm}$ (the negative sign indicates inverted image)

Step3: Characteristics of Image

For a concave mirror, when $d_o > f$ (here, $11.0 > 5.0$), the image is real, inverted, and diminished (since $|h_i| < h_o$).

Step4: Percentage Error (Note: Measured values are needed for error, but since the problem might expect calculated values first, we provide the calculated $d_i$ and $h_i$)

Answer:

Image Distance ($d_i$): $\boldsymbol{\approx 9.17\ \text{cm}}$

Image Height ($h_i$): $\boldsymbol{\approx -1.66\ \text{cm}}$ (inverted, so negative)

Characteristics of Image: Real, Inverted, Diminished