Solved Physics 152 Convex & Concave MIRROR Worksheet The | Chegg.com - Free Printable

It looks like you've uploaded a Concave Mirror Worksheet from a physics class (Physics 152), and the task is to analyze the image formation by a concave mirror for different object distances \( s \) (in terms of focal length \( f \)).

Since I can't see the actual image, I’ll walk you through solving this step-by-step, based on the standard format of such worksheets. You have five cases:

1. \( s = 3f \)
2. \( s = 2f \)
3. \( s = f \)
4. \( s = \frac{1}{2}f \)
5. \( s = \frac{1}{3}f \)

We'll go through each case using:

- Ray diagrams (using the three principal rays),
- Mirror equation:
\[
\frac{1}{f} = \frac{1}{s} + \frac{1}{s'}
\]
- Magnification formula:
\[
m = -\frac{s'}{s} = \frac{y'}{y}
\]

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🔍 Key Concepts for Concave Mirrors

- Focal point (F): at distance \( f \) from the mirror.
- Center of curvature (C): at distance \( 2f \).
- Sign convention:
- Object distance \( s > 0 \) (object in front of mirror).
- Image distance \( s' > 0 \): real image (in front).
- \( s' < 0 \): virtual image (behind).
- Magnification \( m > 0 \): upright; \( m < 0 \): inverted.

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Let’s solve each case.

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## ✔ Case 1: \( s = 3f \)

Step 1: Ray Diagram (3 Principal Rays)

1. Parallel ray: From object, parallel to axis → reflects through focus \( F \).
2. Through focus ray: From object through \( F \) → reflects parallel.
3. Through center ray: From object through \( C \) → reflects back on itself.

These rays converge in front of the mirror → real, inverted image.

Step 2: Use Mirror Equation

\[
\frac{1}{f} = \frac{1}{3f} + \frac{1}{s'}
\Rightarrow \frac{1}{s'} = \frac{1}{f} - \frac{1}{3f} = \frac{2}{3f}
\Rightarrow s' = \frac{3f}{2} = 1.5f
\]

✔ Image distance: \( s' = 1.5f \)

Step 3: Magnification

\[
m = -\frac{s'}{s} = -\frac{1.5f}{3f} = -0.5
\Rightarrow y' = m \cdot y = -0.5y
\]

✔ Image height: \( y' = -0.5y \) → inverted, half size.

✔ Real image (since \( s' > 0 \))

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## ✔ Case 2: \( s = 2f \)

Ray Diagram:

Same three rays → intersect at \( s' = 2f \), same as object.

Mirror Equation:

\[
\frac{1}{f} = \frac{1}{2f} + \frac{1}{s'} \Rightarrow \frac{1}{s'} = \frac{1}{f} - \frac{1}{2f} = \frac{1}{2f}
\Rightarrow s' = 2f
\]

✔ Image distance: \( s' = 2f \)

Magnification:

\[
m = -\frac{2f}{2f} = -1 \Rightarrow y' = -y
\]

✔ Image height: \( y' = -y \) → inverted, same size.

✔ Real image

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## ✔ Case 3: \( s = f \)

Ray Diagram:

- Parallel ray → goes through \( F \)
- Through \( F \) ray → goes parallel
- These two rays are parallel after reflection → never meet.
- The third ray (through \( C \)) reflects back.

→ No image formed (rays diverge, no convergence).

Mirror Equation:

\[
\frac{1}{f} = \frac{1}{f} + \frac{1}{s'} \Rightarrow \frac{1}{s'} = 0 \Rightarrow s' = \infty
\]

✔ Image at infinity.

✔ No finite image — no image formed.

✔ Not real or virtual — image is at infinity.

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## ✔ Case 4: \( s = \frac{1}{2}f \)

Object between \( F \) and mirror.

Ray Diagram:

- Parallel ray → reflects through \( F \)
- Through \( F \) ray → reflects parallel
- These diverge → appear to come from behind mirror.
- Third ray (through \( C \)) → reflects back.

→ Virtual, upright image behind mirror.

Mirror Equation:

\[
\frac{1}{f} = \frac{1}{0.5f} + \frac{1}{s'} = \frac{2}{f} + \frac{1}{s'}
\Rightarrow \frac{1}{s'} = \frac{1}{f} - \frac{2}{f} = -\frac{1}{f}
\Rightarrow s' = -f
\]

✔ Image distance: \( s' = -f \) → virtual

Magnification:

\[
m = -\frac{s'}{s} = -\frac{-f}{0.5f} = \frac{f}{0.5f} = 2
\Rightarrow y' = 2y
\]

✔ Image height: \( y' = 2y \) → upright, magnified

✔ Virtual image

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## ✔ Case 5: \( s = \frac{1}{3}f \)

Even closer to mirror.

Ray Diagram:

Similar to previous — rays diverge after reflection → virtual image behind mirror.

Mirror Equation:

\[
\frac{1}{f} = \frac{1}{(1/3)f} + \frac{1}{s'} = \frac{3}{f} + \frac{1}{s'}
\Rightarrow \frac{1}{s'} = \frac{1}{f} - \frac{3}{f} = -\frac{2}{f}
\Rightarrow s' = -\frac{f}{2}
\]

✔ Image distance: \( s' = -0.5f \)

Magnification:

\[
m = -\frac{s'}{s} = -\frac{-0.5f}{(1/3)f} = \frac{0.5}{1/3} = 1.5
\Rightarrow y' = 1.5y
\]

✔ Image height: \( y' = 1.5y \) → upright, magnified

✔ Virtual image

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📊 Summary Table

| Object Distance | Image Distance \( s' \) | Image Height \( y' \) | Real/Virtual | Upright/Inverted |
|------------------|----------------------------|-------------------------|---------------|--------------------|
| \( s = 3f \) | \( 1.5f \) | \( -0.5y \) | Real | Inverted |
| \( s = 2f \) | \( 2f \) | \( -y \) | Real | Inverted |
| \( s = f \) | \( \infty \) | \( \infty \) | Not formed | — |
| \( s = 0.5f \) | \( -f \) | \( 2y \) | Virtual | Upright |
| \( s = 0.33f \) | \( -0.5f \) | \( 1.5y \) | Virtual | Upright |

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✔ How to Draw the Ray Diagrams (on worksheet)

For each case:

1. Draw the concave mirror with labeled points: F (focus), C (center of curvature).
2. Place the object (arrow) at the given distance.
3. Draw three rays:
- From top of object:
- Parallel to axis → reflect through \( F \)
- Through \( F \) → reflect parallel
- Through \( C \) → reflect back on itself
4. Where they intersect → image location.
- If rays converge in front → real image.
- If diverge → extend backward → virtual image.

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Final Notes:

- For \( s > f \): Real, inverted images.
- At \( s = f \): No image.
- For \( s < f \): Virtual, upright, magnified images.

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If you'd like, I can generate a text-based sketch of one of the ray diagrams or help you label the worksheet. Let me know!