Find the angle at which two plane mirrors are kept inclined, if the following number of images
are formed for an object kept between them :- (i) 8 (ii) 11 (iii) 3 (iv) 5
Answers
Explanation:
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.
