91影视

• Distance between two parallel plane mirrors is$40\text{cm}$.
• Distance between object and first mirror is $10\text{cm}$.

As two plane mirrors are placed parallel to each other separated by a distance of $\mathbf{40}\mathbf{\text{cm}}$, they will form images as shown in the below diagram. Each mirror produces a first image of the object. Then, each mirror produces a second image with the object being the first image in the opposite mirror. Then each mirror produces a third image with the object being the second image in the opposite mirror, and so on. Therefore, the mirrors will produce five images. Here, you find the smallest distance, second smallest distance, third smallest distance, and fourth smallest distance between the object and an image of the object.

To know the smallest distance, yourefer the above figure. In the closest mirror$M_1$, the 鈥渇irst鈥� image$I_1$is $10\text{cm}$ behindrole="math" localid="1663022915939" $M_1$and thus,$20\text{cm}$ from the object O. This is the smallest distance between the object and an image of the object.

Hence, the smallest distance is $20\text{cm}$.

To know the second smallest distance, refer the above figure. There are images from both Oand$I_1$in the more distant mirror,$M_2$an image$I_2$located at $30\text{cm}$behind$M_2$. Since Ois $30\text{cm}$ in front of it,$I_2$is $60\text{cm}$ from O. This is the second smallest distance between the object and an image of the object.

Hence, the second smallest distance is $60\text{cm}$.

To know the third smallest distance, refer the above figure. There is also an image $I_3$that is $50\text{cm}$behind $M_2$ (since $I_1$ is $50\text{cm}$ in front of it). Thus, $I_3$is $80\text{cm}$from O. In addition, you have another image $I_4$that is $70\text{cm}$ behind role="math" localid="1663023685109" $M_1$ (since $I_2$ is $70\text{cm}$ in front of it). The distance from $I_4$ to O for is $80\text{cm}$.

Hence, the third smallest distance is $80\text{cm}$.

To know the fourth smallest distance, yourefer the above figure. Returning to the closer mirror$M_1$, there is an image$I_5$that is $90\text{cm}$ behind the mirror (sincerole="math" localid="1663023840894" $I_3$is $90\text{cm}$ in front of it). The distance (measured from O) is found to be $100\text{cm}$for$I_5$.

Hence, the fourth smallest distance is $100\text{cm}$.