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 use the formula for the number of images formed by two inclined mirrors.

### Step-by-Step Solution:

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

2. **Setting Up the Equation**:
We know from the problem that the number of images (n) is 7. Therefore, we can set up the equation:
\[ 7 = \frac{360^\circ}{\theta} - 1 \]

3. **Rearranging the Equation**:
To isolate the term involving θ, we can add 1 to both sides of the equation:
\[ 7 + 1 = \frac{360^\circ}{\theta} \]
This simplifies to:
\[ 8 = \frac{360^\circ}{\theta} \]

4. **Cross-Multiplying**:
Now, we can cross-multiply to solve for θ:
\[ 8\theta = 360^\circ \]

5. **Dividing to Find θ**:
To find θ, divide both sides by 8:
\[ \theta = \frac{360^\circ}{8} \]

6. **Calculating the Final Value**:
Performing the division gives:
\[ \theta = 45^\circ \]

### Final Answer:
The angle between the two mirrors is \( \theta = 45^\circ \).

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