Question:
Two plane mirrors \(A\) and \(B\) are placed parallel to each other with a separation of \(2\,\text{m}\) between them. If an object is placed between the mirrors at a distance of \(60\,\text{cm}\) from mirror \(B\), then the distance of the second nearest image seen in mirror \(B\) from mirror \(A\) is
\[
(\text{The reflecting surfaces of the two mirrors face each other})
\]
Two plane mirrors \(A\) and \(B\) are placed parallel to each other with a separation of \(2\,\text{m}\) between them. If an object is placed between the mirrors at a distance of \(60\,\text{cm}\) from mirror \(B\), then the distance of the second nearest image seen in mirror \(B\) from mirror \(A\) is
\[
(\text{The reflecting surfaces of the two mirrors face each other})
\]
Show Hint
For two parallel plane mirrors separated by distance \(d\), successive images are formed at intervals of
\[
\boxed{2d}
\]
behind each mirror.
Updated On: Jul 18, 2026
- \(3.4\,\text{m}\)
- \(5.4\,\text{m}\)
- \(2.6\,\text{m}\)
- \(4.6\,\text{m}\)
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Locate the object.
The mirrors are separated by
\[
d=2\,\text{m}.
\]
The object is
\[
0.6\,\text{m}
\]
from mirror \(B\).
Hence, its distance from mirror \(A\) is
\[
2-0.6=1.4\,\text{m}.
\]
Step 2: Use the image positions in two parallel mirrors. The images seen in mirror \(B\) are formed behind mirror \(B\) at distances \[ 0.6,\;3.4,\;4.6,\;7.4,\ldots\text{ m} \] from mirror \(B\). Therefore, the second nearest image behind mirror \(B\) is at \[ 3.4\,\text{m} \] behind mirror \(B\).
Step 3: Measure its distance from mirror \(A\). Since mirror \(A\) and mirror \(B\) are \[ 2\,\text{m} \] apart, \[ \text{Distance from mirror }A = 2+3.4 = 5.4\,\text{m}. \] Hence, \[ \boxed{5.4\,\text{m}.} \] Therefore, the correct option is \(\boxed{(B)}\).
Step 2: Use the image positions in two parallel mirrors. The images seen in mirror \(B\) are formed behind mirror \(B\) at distances \[ 0.6,\;3.4,\;4.6,\;7.4,\ldots\text{ m} \] from mirror \(B\). Therefore, the second nearest image behind mirror \(B\) is at \[ 3.4\,\text{m} \] behind mirror \(B\).
Step 3: Measure its distance from mirror \(A\). Since mirror \(A\) and mirror \(B\) are \[ 2\,\text{m} \] apart, \[ \text{Distance from mirror }A = 2+3.4 = 5.4\,\text{m}. \] Hence, \[ \boxed{5.4\,\text{m}.} \] Therefore, the correct option is \(\boxed{(B)}\).
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