Review the key concepts, formulae, and examples before starting your quiz.
πConcepts
When two plane mirrors are kept at an angle to each other, they form multiple images. This happens because the image formed by one mirror acts as an object for the second mirror.
The number of images formed depends on the angle between the two mirrors.
If the two mirrors are placed parallel to each other (where ), the number of images formed is infinite.
A Kaleidoscope is an optical instrument that works on the principle of multiple reflections. It typically consists of three plane mirrors inclined at an angle of to each other.
In a Kaleidoscope, the arrangement of mirrors produces beautiful, symmetrical, and ever-changing patterns because no two patterns are exactly the same when the tube is rotated.
Designers of wallpapers, fabrics, and artists often use kaleidoscopes to get ideas for new patterns.
πFormulae
π‘Examples
Problem 1:
Calculate the number of images formed if two plane mirrors are placed at an angle of to each other.
Solution:
Explanation:
Using the formula for multiple reflections, dividing by the angle gives . Subtracting from this result gives images.
Problem 2:
If a Kaleidoscope uses three mirrors inclined at an angle of , how many images of a single object inside will be formed by any two mirrors?
Solution:
Explanation:
Since the mirrors in a standard kaleidoscope are usually at , the number of images formed by the intersection of two mirrors is .
Problem 3:
Two mirrors are kept parallel to each other. How many images will be seen for an object placed between them?
Solution:
Explanation:
When mirrors are parallel, the angle is . Since division by zero approaches infinity, an infinite number of images are formed due to continuous reflections between the surfaces.