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An object "O" is placed between two parallel mirrors as shown in fig. find the seperation between nth order images

Asked by sirib942254 | 15 Jul, 2021, 05:32: PM
Expert Answer
 
Let us consider left mirror LM and right mirror RM as shown in figure.
Let O be the position of object at a distance a from right mirror and b from left mirror
 
First order image :-
Image B is at a distance a at the back side of RM , hence at a distance 2a from O
Image A is at a distance b at the back side of LM , hence at a distance 2b from O
Hence distance between A and B,  AB = 2(a+b)
 
Second order image :-
B' is image of B , hence B' is at a distance (2a+b) at the back side of LM , hence at a distance (2a+2b) from O
A' is Image of A,  hence A' is at a distance (2b+a) at the back side of RM , hence at a distance (2b+2a) from O
Hence distance between A' and B' ,  A'B' = 4(a+b)
 
Third order image :-
B'' is image of B' , hence B'' is at a distance (3a+2b) at the back side of RM , hence at a distance (4a+2b) from O
A'' is Image of A',  hence A'' is at a distance (3b+2a) at the back side of LM , hence at a distance (4b+2a) from O
Hence distance between A'' and B'' ,  A''B'' = 6(a+b)
 
Hence distance between nth order images = 2n(a+b)
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