Number of images of an object kept symmetrically between two mirrors inclined at angle `72^(@)`, would be

Options

A. 5
B. 4
C. 2
D. infinite

Answer

To find the number of images formed by two mirrors inclined at an angle of \(72^\circ\) when an object is placed symmetrically between them, we can use the formula for the number of images \(n\) created by two plane mirrors inclined at an angle \(\theta\):

\[ n = \frac{360^\circ}{\theta} - 1 \]

### Step-by-step Solution:

1. **Identify the angle of inclination**:
The angle \(\theta\) between the two mirrors is given as \(72^\circ\).

2. **Substitute the angle into the formula**:
We substitute \(\theta\) into the formula for the number of images:
\[ n = \frac{360^\circ}{72^\circ} - 1 \]

3. **Calculate \(\frac{360^\circ}{72^\circ}\)**:
Perform the division:
\[ \frac{360}{72} = 5 \]

4. **Subtract 1 from the result**:
Now, subtract 1 from the result obtained in the previous step:
\[ n = 5 - 1 = 4 \]

5. **Conclusion**:
Therefore, the number of images formed is \(4\).

### Final Answer:
The number of images of the object kept symmetrically between two mirrors inclined at an angle of \(72^\circ\) is \(4\).

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