## Step-by-Step Ray Tracing for Concave Mirror Let’s analyze each object position using the **ray tracing method**. For each case, we’ll: 1. **Draw at least two principal rays** to locate the image. 2. **Describe the image's position and nature** (real/virtual, inverted/upright, magnified/reduced). --- ### **1. Object Beyond C (Center of Curvature)** **Step 1: Ray Tracing** - Draw a ray parallel to the principal axis — it reflects through the focus (F). - Draw a ray through the focus (F) — it reflects parallel to the principal axis. - **Intersection of reflected rays:** Between C and F. **Step 2: Image Description** - **Position:** Between C and F. - **Nature:** Real, inverted, and smaller than the object. --- ### **2. Object at C (Center of Curvature)** **Step 1: Ray Tracing** - Draw a parallel ray (reflects through F) and a ray through F (reflects parallel). - **Intersection:** At C. **Step 2: Image Description** - **Position:** At C. - **Nature:** Real, inverted, and same size as the object. --- ### **3. Object Between C and F (Focus)** **Step 1: Ray Tracing** - Draw a parallel ray (reflects through F) and a ray through F (reflects parallel). - **Intersection:** Beyond C. **Step 2: Image Description** - **Position:** Beyond C. - **Nature:** Real, inverted, and magnified. --- ### **4. Object at F (Focus)** **Step 1: Ray Tracing** - Draw a parallel ray (reflects through F) and a ray through C (reflects back along itself). - The reflected rays are **parallel and never meet**. **Step 2: Image Description** - **Position:** At infinity. - **Nature:** No real image is formed; image is highly enlarged. --- ### **5. Object Between F (Focus) and Mirror** **Step 1: Ray Tracing** - Draw a parallel ray (reflects through F) and a ray heading towards F (reflects parallel). - Reflected rays **diverge**—trace them backward; they appear to meet **behind the mirror**. **Step 2: Image Description** - **Position:** Behind the mirror. - **Nature:** Virtual, upright, and magnified. --- ## **Final Summary Table** | Object Position | Image Position | Real/Virtual | Inverted/Upright | Magnification | |---------------------|--------------------|--------------|------------------|------------------| | Beyond C | Between C and F | Real | Inverted | Reduced | | At C | At C | Real | Inverted | Same size | | Between C and F | Beyond C | Real | Inverted | Enlarged | | At F | At infinity | - | - | Highly enlarged | | Between F and Mirror| Behind mirror | Virtual | Upright | Enlarged | These results follow from the **ray tracing method** for concave spherical mirrors.