Answer:
D. Infinite
Explanation:
When an object is placed between two parallel plane mirrors, each inclined at an angle \( \theta \) to the other, the formula for calculating the total number of images formed is given by:
[tex]\[ N = \frac{360°}{|\theta| - 180°} \][/tex]
[tex]In this case, ( \theta = 72\° ).[/tex]
[tex]\[ N = \frac{360°}{|72°| - 180°} \][/tex]
[tex]\[ N = \frac{360°}{72° - 180°} \][/tex]
[tex]\[ N = \frac{360°}{-108°} \][/tex]
[tex]\[ N = -\frac{360°}{108°} \][/tex]
[tex]\[ N = -\frac{30}{9} \][/tex]
[tex]\[ N = -\frac{10}{3} \][/tex]
The total number of images formed is a fraction, which is not a meaningful result for the number of images. In the context of multiple mirrors, the fraction indicates that the images repeat in a periodic manner.
However, it's important to note that the number of images formed in such a setup is not a whole number. Therefore, the concept of an exact "total number of images" may not be applicable in this case.
If you are looking for the closest whole number, you might consider the integer value closest to the fraction. In this case, the closest integer to [tex]\( -\frac{10}{3} \)[/tex]
So, the total number of images formed is closest to -3, but keep in mind that this is not a typical scenario for counting reflections between two mirrors. The fraction indicates a repeating pattern rather than a finite number of distinct images.
D. Infinite
The total number of images formed is infinite.
When an object is placed symmetrically between two plane mirrors inclined at an angle of 72°, the total number of images formed is infinite.
This is because each mirror will reflect the image formed by the other mirror, creating a chain of images that goes on infinitely.
Therefore, the correct answer is D. Infinite.
