Question

Two plane mirrors are inclined at angle 40° between them Number of images seen of tiny
object kept at bisector is-
O
8
O
10
O 9
O 7​

Answer 1

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.

Answer 2

Number of images seen of tiny  object kept at bisector is $8$.

Explanation:

• When two plane mirrors are kept together at a certain angle, then the there are formation of multiple images.
• Inclined mirrors form images in a circle. And the circle is divided into multiple sectors.
• Number of sector will be decided by the angle at which both the mirrors are inclined.
• Number of sector $(N)$ is expressed by $\frac{360}{x}$ where x is the angle of inclination of the two mirrors.
• Then, number of images ($n$) formed can be calculated by:

$n=(\frac{360}{x} )-1$  

, Where $x$ is the degree at which both the mirrors are inclined i.e. the angle made between both the mirrors.

• 1 is subtracted from the number of sector because object itself will occupy one of the sector in the circle.
• The angle of inclination here is $40^{o}$. So, number of images will be:

$n=(\frac{360}{x} )-1$

$n=\frac{360}{40} -1=9-1=8$

So, number images are $8$.