Question

Chapter- Light

Find the angle of inclination between two mirrors . if number of image formed by the mirror is 5 .

Answer 1

$\begin{gathered}\\\;\underbrace{\underline{\sf{\;Question\;:-}}}\end{gathered}$

Find the angle of inclination between two mirrors . if number of image formed by the mirror is 5 .

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★ Formula Used :-

$\begin{gathered}\begin{gathered}\begin{gathered}\\\;\boxed{\sf{\pink{n\;=\;\bf{\bigg(\;\dfrac{360 - 1 }{ \theta}\bigg)}}}}\end{gathered} \end{gathered}\end{gathered}$

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★ Solution :-

Given,

» No. image formed by the mirror = 5

To find ,

» angle of inclination between two mirrors

~ Let's find it ,

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we know that ,

$\begin{gathered}\begin{gathered}\begin{gathered}\\\;{\sf{{n \:\;=\;\bf{\bigg(\;\dfrac{360 - 1 }{ \theta}\bigg)}}}}\end{gathered} \end{gathered}\end{gathered}$

Note - n is the Number of image formed by the mirror

Let's put the value of n

$\begin{gathered}\begin{gathered}\begin{gathered}\\\; \longrightarrow{\sf{{7 \:\;=\;\bf{\bigg(\;\dfrac{360 - 1 }{ \theta}\bigg)}}}}\end{gathered} \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\\\; \longrightarrow{\sf{{7 + 1 \:\;=\;\bf{\bigg(\;\dfrac{360 }{ \theta}\bigg)}}}}\end{gathered} \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\\\; \longrightarrow{\sf{{8\:\;=\;\bf{\bigg(\;\dfrac{360 }{ \theta}\bigg)}}}}\end{gathered} \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\\\; \longrightarrow{\sf{{ \theta\:\;=\;\bf{\bigg(\;\dfrac{360 }{ 8}\bigg)}}}}\end{gathered} \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\\\; \Longrightarrow{\sf{{ \green{ \theta\:\;=\;\bf{\;45 \degree}}}}}\end{gathered} \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\\\;\underline{\boxed{\tt{\odot\;\;Hence,\;\;angle \: of\;inclination=\;\bf{\blue{45\degree}}}}}\end{gathered} \end{gathered}\end{gathered}$

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★ More to know :-

Multiple Images -

• Multiple images can be made from two plane mirror due to multiple reflections .

• When two plane mirrors are inclined at the angle of an object is placed between them , then many and images of the object are formed

Reason -

• This is because image formed by one mirror acts as the object for the other mirror .

• The number of image formed depends upon the angle at which two mirrors are inclined .

The number of images formed can be calculated from the following formula :-

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\\\;\sf{\gray{\leadsto\;\; {n\;=\;\bf{\bigg(\;\dfrac{360 - 1 }{ \theta}\bigg)}}}}\end{gathered} \end{gathered} \end{gathered} \end{gathered}$

Where n is the Number of image formed by the mirror and θ is the angle of inclination between two mirror

Answer 2

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