Question

A point object is placed mid-way between two plane mirrors which are $a$ distance apart. The plane mirrors forms an infinite number of images due to multiple reflections. The distance between the $n^{\text{th}}$ order image (i.e $n^{th}$ image in both the mirrors) formed in the two mirrors is

• A. $8na$
• B. $2na$
• C. $4na$
• D. $6na$

Answer 1

The correct option is B $2na$


The distance between $1^{\text{st}}$ order images ($I_1$ and $I_1^{{}^{\prime }}$) will be,
$d_1=\frac{a}{2}+\frac{a}{2}+a=2a$
The distance between $2^{\text{nd}}$ order images ($I_2$ and $I_2^{{}^{\prime }}$) will be,
$d_2=\frac{3a}{2}\times 2+a=4a$
Similarly, the distance between $3^{\text{rd}}$ order images ($I_3$ and $I_3^{{}^{\prime }}$) will be,
$d_3=\frac{5a}{2}\times 2+a=6a$
Based on the above pattern, the distance between $n^{\text{th}}$ order images will be,
$d_n=\frac{(2n-1)a}{2}\times 2+a=2na$