If two mirrors are inclined at some angle and an object is placed between the mirrors and there are 7 images formed for an object, then the angle between the mirrors is

Options

A. `54^@`
B. `45^@`
C. `60^@`
D. `64^@`

Answer

To solve the problem of finding the angle between two mirrors that form 7 images of an object placed between them, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The number of images (n) formed by two mirrors inclined at an angle (θ) is given by the formula:
\[ n = \frac{360}{\theta} - 1 \]

2. **Set Up the Equation**: Given that the number of images (n) is 7, we can substitute this value into the formula:
\[ 7 = \frac{360}{\theta} - 1 \]

3. **Rearrange the Equation**: To isolate the term involving θ, we first add 1 to both sides:
\[ 7 + 1 = \frac{360}{\theta} \]
\[ 8 = \frac{360}{\theta} \]

4. **Solve for θ**: Now, we can solve for θ by multiplying both sides by θ and then dividing both sides by 8:
\[ 8\theta = 360 \]
\[ \theta = \frac{360}{8} \]

5. **Calculate the Angle**: Performing the division gives us:
\[ \theta = 45^\circ \]

6. **Conclusion**: Therefore, the angle between the two mirrors is:
\[ \theta = 45^\circ \]

### Final Answer:
The angle between the mirrors is **45 degrees**.

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