State the number of images of an object placed between the two plane mirrors, formed in each case when the mirrors are inclined to each other at a. `90^(@)`, and b `60^(@)`

Answer

To determine the number of images formed by an object placed between two plane mirrors inclined at different angles, we can use the formula:

\[ \text{Number of images} = \frac{360}{\theta} - 1 \]

where \(\theta\) is the angle between the two mirrors.

### Step-by-Step Solution:

**Step 1: Identify the angle for the first case.**
- For the first case, the mirrors are inclined at an angle of \(90^\circ\).

**Step 2: Apply the formula for the first case.**
- Substitute \(\theta = 90^\circ\) into the formula:
\[ \text{Number of images} = \frac{360}{90} - 1 \]
- Calculate:
\[ \frac{360}{90} = 4 \]
- Therefore:
\[ \text{Number of images} = 4 - 1 = 3 \]

**Step 3: Identify the angle for the second case.**
- For the second case, the mirrors are inclined at an angle of \(60^\circ\).

**Step 4: Apply the formula for the second case.**
- Substitute \(\theta = 60^\circ\) into the formula:
\[ \text{Number of images} = \frac{360}{60} - 1 \]
- Calculate:
\[ \frac{360}{60} = 6 \]
- Therefore:
\[ \text{Number of images} = 6 - 1 = 5 \]

**Final Answer:**
- For the mirrors inclined at \(90^\circ\), the number of images formed is **3**.
- For the mirrors inclined at \(60^\circ\), the number of images formed is **5**.