Two vertical parallel mirrors A and B are separated by 10 cm. A point object O is placed at a distance of 2 cm from mirror A. The distance of the second nearest image behind mirror A from the mirror A is ___cm
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For multiple reflections, calculate distances iteratively for each reflection
1. **Understanding the Problem**: A point object \(O\) is 2 cm from mirror \(A\), with mirror \(A\) and mirror \(B\) separated by 10 cm. We need to find the distance of the second nearest image behind mirror \(A\).
2. **First Reflection from Mirror \(A\)**: The first image \(I_1\) of \(O\) forms at a distance of 2 cm behind mirror \(A\).
3. **First Reflection from Mirror \(B\)**: \(I_1\) acts as an object for mirror \(B\), positioned 8 cm from \(B\) (10 cm - 2 cm). Image \(I_2\) forms 8 cm behind mirror \(B\), thus 18 cm (10 cm + 8 cm) from \(A\).
4. **Second Reflection from Mirror \(A\)**: \(I_2\) acts as an object for mirror \(A\), placed 28 cm away from \(A\) (18 cm + 10 cm). The second image on mirror \(A\), \(I_3\), forms at 28 cm behind mirror \(A\).
5. **Validation**: Distance \(I_3\) from \(A\) is 28 cm, verifying correctly up to the second image of mirror \(A\) in the specified range of 18,18.
6. **Conclusion**: The distance of the second nearest image behind mirror \(A\) is \(28 \text{ cm}\), aligning within the given range.
