We know that a plane mirror forms only a single image of an
object placed in front of it. We will now describe what happens
when an object is placed between two plane mirrors which are
inclined at an angle to each other. When two plane mirrors are
kept inclined at an angle, they can form multiple images of an
object. This is because the image of object formed in one plane
mirror acts as object for the other plane mirror. It has been found
that if two plane mirrors are inclined at an angle x, then the
number of images formed in them is given by the formula :
360°
No. of images formed - 1
By using this formula, we can calculate the number of images
formed (or seen) when two plane mirrors are inclined at angles
of 180°, 120°, 90°, 60°, 45° and 0°, respectively.
i). How can we get multiple images of an object?
ii) Why this multiple images are formed?
iii) Write the formula of number of images formed.
iv) What will be the number of images formed when an object is
placed between two parallel plane mirrors facing each other?
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Answers
Answer:
If the image of an object is viewed in two plane mirrors that are inclined to each other more than one image is formed. The number of images depends on the angle between the two mirrors.
The number of images formed in two plane mirrors inclined at an angle A to each other is given by the below formula.Number of images n= 360/A - 1
The number of images formed n=(360/A)-1, if (360/A) is even integer.If (360/A) is odd integer, the number of images formed n=(360/A)-1 when the object is kept symmetrically, and n=(360/A) when object is kept asymmetrically.
If (360/A) is a fraction, the number of images formed is equal to its integral part.
As the angle gets smaller (down to 0 degrees when the mirrors are facing each other and parallel) the smaller the angle the greater the number of images.
Here, the angle A between the mirrors is 40 degrees.
Case (a): The object is symmetrically placed.
The number of images formed = (360/40)-1, we get 8 images.
Case (b): The object is asymmetrically placed.
The number of images formed = (360/40), we get 9 images.
Hence, the number of images formed are 8 and 9 respectively.
Explanation:
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