A person is in a room whose ceiling and two adjacent walls are mirrors. How many images are formed

Options

A. 5
B. 6
C. 7
D. 8

Answer

To determine how many images are formed when a person is in a room with mirrors on the ceiling and two adjacent walls, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Mirrors**:
- We have three mirrors in total:
- Mirror M1 (the ceiling)
- Mirror M2 (one wall)
- Mirror M3 (the adjacent wall)

2. **Understand the Geometry**:
- The two adjacent walls (M2 and M3) form a 90-degree angle with each other.

3. **Calculate Images from Adjacent Walls**:
- The formula for the number of images formed by two mirrors at an angle θ is given by:
\[ N = \frac{360}{\theta} - 1 \]
- For our case, θ = 90 degrees:
\[ N = \frac{360}{90} - 1 = 4 - 1 = 3 \]
- Thus, the two adjacent walls (M2 and M3) will produce 3 images.

4. **Calculate Images from the Ceiling**:
- The ceiling (M1) will reflect all the images formed by the walls. Since there are 3 images from the walls, each of these images will act as an object for the ceiling mirror.
- The ceiling will also create images of these 3 images. Each of these images will produce 2 additional images (one above and one below), leading to:
\[ \text{Total images from ceiling} = 3 \text{ (images from walls)} \times 2 = 6 \]

5. **Total Images Calculation**:
- Now, we sum the images from the walls and the ceiling:
\[ \text{Total Images} = \text{Images from walls} + \text{Images from ceiling} + \text{Original object} \]
- Therefore:
\[ \text{Total Images} = 3 + 6 + 1 = 10 \]

### Final Answer:
The total number of images formed is **10**.

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