An object shaped as L is placed between two p | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) When an object is placed between two parallel plane mirrors,multiple images are formed due to successive reflections.Let the mirrors be $M_1$ and

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) When an object is placed between two parallel plane mirrors,multiple images are formed due to successive reflections.Let the mirrors be $M_1$ and $M_2$. An image formed by a single reflection in a plane mirror is laterally inverted.If an image is formed by an even number of reflections,it is not laterally inverted (it is erect relative to the original object).If an image is formed by an odd number of reflections,it is laterally inverted.Let the object be at a distance $d_1$ from $M_1$ and $d_2$ from $M_2$. The images formed by $M_1$ are at distances $d_1, 2d_2+d_1, 2d_1+2d_2+d_1, \dots$ and those by $M_2$ are at $d_2, 2d_1+d_2, 2d_2+2d_1+d_2, \dots$.Counting the first seven images in order of distance:$1$. $I_1$ (from $M_1$): $1$ reflection (odd) $\rightarrow$ Laterally inverted.$2$. $I_2$ (from $M_2$): $1$ reflection (odd) $\rightarrow$ Laterally inverted.$3$. $I_3$ (from $M_2$ via $M_1$): $2$ reflections (even) $\rightarrow$ Not laterally inverted.$4$. $I_4$ (from $M_1$ via $M_2$): $2$ reflections (even) $\rightarrow$ Not laterally inverted.$5$. $I_5$ (from $M_1$ via $M_2$ via $M_1$): $3$ reflections (odd) $\rightarrow$ Laterally inverted.$6$. $I_6$ (from $M_2$ via $M_1$ via $M_2$): $3$ reflections (odd) $\rightarrow$ Laterally inverted.$7$. $I_7$ (from $M_2$ via $M_1$ via $M_2$ via $M_1$): $4$ reflections (even) $\rightarrow$ Not laterally inverted.Thus,in the first seven images,the images $I_1, I_2, I_5, I_6$ are laterally inverted. Total count is $4$.

An object shaped as $L$ is placed between two parallel plane mirrors as shown. In the first seven closest images,how many laterally inverted images are formed?

Similar Questions

$A$ man of height $h$ requires a mirror to see his own complete image. The minimum height of the mirror required is:

$A$ person is in a room whose ceiling and two adjacent walls are mirrors. How many images are formed?

The light reflected by a plane mirror may form a real image:

$A$ tall man of height $6$ feet wants to see his full image. The required minimum length of the mirror will be ......... feet.

Vedclass Test Series

Exam Paper Generator

Online Exam Module