Two mirrors placed at an angle to `theta` each other form 23 images of an object placed in between them. What is the value of angle `theta` ?

Options

A. `15^@`
B. `30^@`
C. `45^@`
D. `60^@`

Answer

To solve the problem of finding the angle \( \theta \) between two mirrors that form 23 images of an object placed between them, we can follow these steps:

### Step 1: Understand the formula for the number of images
The number of images \( N \) formed by two mirrors placed at an angle \( \theta \) is given by the formula:
\[ N = \frac{360}{\theta} - 1 \]

### Step 2: Set up the equation
We know from the problem that the number of images \( N \) is 23. Therefore, we can set up the equation:
\[ 23 = \frac{360}{\theta} - 1 \]

### Step 3: Rearrange the equation
To isolate \( \theta \), we first add 1 to both sides:
\[ 23 + 1 = \frac{360}{\theta} \]
\[ 24 = \frac{360}{\theta} \]

### Step 4: Solve for \( \theta \)
Now, we can cross-multiply to solve for \( \theta \):
\[ 24\theta = 360 \]
Now, divide both sides by 24:
\[ \theta = \frac{360}{24} \]

### Step 5: Calculate the value of \( \theta \)
Now, we perform the division:
\[ \theta = 15 \]

### Conclusion
The angle \( \theta \) between the two mirrors is \( 15^\circ \).

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