Which of these formulae correctly depicts the relationship between the angle between two plane mirrors and the number of images that will be formed within them if an object is placed between them?

Options

A. `n=1-(360^@//theta)`
B. `n=1(360^@//theta)-1`
C. `n=(360^@//theta)+1`
D. `n=360^@//theta`

Answer

To solve the question regarding the relationship between the angle between two plane mirrors and the number of images formed, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept**: When an object is placed between two plane mirrors, multiple images of the object are formed due to the reflection of light. The number of images depends on the angle between the two mirrors.

2. **Identify the Formula**: The formula that relates the angle (θ) between the two mirrors and the number of images (n) formed is given by:
\[ n = \frac{360^\circ}{\theta} - 1 \]
Here, \( n \) is the number of images, and \( \theta \) is the angle between the two mirrors.

3. **Explanation of the Formula**:
- The total angle in a circle is 360 degrees.
- By dividing 360 degrees by the angle θ, we determine how many times the angle fits into a full circle.
- We subtract 1 because the original object is counted as one of the images.

4. **Examples**:
- If the angle θ is 10 degrees, the number of images would be:
\[ n = \frac{360^\circ}{10^\circ} - 1 = 36 - 1 = 35 \]
- If θ is 30 degrees, then:
\[ n = \frac{360^\circ}{30^\circ} - 1 = 12 - 1 = 11 \]

5. **Conclusion**: The correct formula that depicts the relationship between the angle between two plane mirrors and the number of images formed is:
\[ n = \frac{360^\circ}{\theta} - 1 \]

### Final Answer:
The correct formula is \( n = \frac{360^\circ}{\theta} - 1 \).

---