Question

Two plane mirrors kept at some angle with each other produce 5 images of any object kept between them. If the angle is decreased by 30°, then the number of images will be

• A. 9
• B. 10
• C. 11
• D. 12

Hint:

To find the number of images produced by two plane mirrors, use the formula \( n = \frac{360^\circ}{\theta} - 1 \), where \( \theta \) is the angle between the mirrors.

Answer 1

The Correct Option is C

Step 1: Use the formula for the number of images produced by two mirrors.
The number of images \( n \) produced by two plane mirrors is
given by the formula:
\[ n = \frac{360^\circ}{\theta} - 1 \] where \( \theta \) is the angle between the mirrors.
Step 2: Apply the initial condition.
Initially, 5 images are produced, so: \[ \frac{360^\circ}{\theta} - 1 = 5 \] \[ \frac{360^\circ}{\theta} = 6 \quad \Rightarrow \quad \theta = 60^\circ \]
Step 3: Change the angle.
Now, the angle is decreased by 30°, so the new angle is: \[ \theta' = 60^\circ - 30^\circ = 30^\circ \]
Step 4: Calculate the new number of images.
Using the formula for the new angle: \[ n' = \frac{360^\circ}{30^\circ} - 1 = 12 - 1 = 11 \]
Step 5: Conclusion.
Thus, the number of images will be 11.
Conclusion:
The correct answer is (C) 11.