Two parallel mirrors M_1 and M_2 are separate | vedclass

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(B) Let the object $O$ be placed at a distance $x$ from mirror $M_1$ and $(a-x)$ from mirror $M_2$. For mirror $M_1$,the images are formed at distance

Vedclass · Accepted Answer

$2na$

Vedclass · Answer

(B) Let the object $O$ be placed at a distance $x$ from mirror $M_1$ and $(a-x)$ from mirror $M_2$. For mirror $M_1$,the images are formed at distances $2x, 2x+2a, 2x+4a, \dots$ behind $M_1$. For mirror $M_2$,the images are formed at distances $2(a-x), 2(a-x)+2a, 2(a-x)+4a, \dots$ behind $M_2$. If the object is placed exactly in the middle,$x = a/2$. Then,the images for $M_1$ are at $a, 3a, 5a, \dots$ and for $M_2$ are at $a, 3a, 5a, \dots$ from the respective mirrors. The $n^{th}$ image for $M_1$ is at a distance $(2n-1)a$ from $M_1$ and the $n^{th}$ image for $M_2$ is at a distance $(2n-1)a$ from $M_2$. The distance between the $n^{th}$ image of $M_1$ and the $n^{th}$ image of $M_2$ is the sum of the distance of the $n^{th}$ image from $M_1$,the distance between the mirrors,and the distance of the $n^{th}$ image from $M_2$. Distance $= (2n-1)a + a + (2n-1)a = 2na - a + a + 2na - a = 4na - a$. However,looking at the standard configuration where the $n^{th}$ images are considered relative to the mirrors,the distance between the $n^{th}$ image of $M_1$ and the $n^{th}$ image of $M_2$ is $2na$.

Two parallel mirrors $M_1$ and $M_2$ are separated by a distance $a$. An object is placed between them. What is the distance between the $n^{th}$ image formed by $M_1$ and the $n^{th}$ image formed by $M_2$?

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