Question

(1) Two plane mirrors are inclined at an angle 400 between them. Number of images seen of a tiny object kept between them is
(a) Only 8 b) Only 9 ( (c)8 or 9 (d) 9 or 10​

Answer 1

Given

• θ = 40°

To Find

• Number of images formed

Solution

☯ Number of images = (360/θ) - 1

• Here the value of θ is 40° as the mirrors are inclined at an angle of 40°

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✭ According to the Question :

➞ Number of images = (360/θ) - 1

➞ Number of images = (360/40) - 1

➞ Number of images = (36/4) - 1

➞ Number of images = 9 - 1

➞ Number of images = 8

∴ The answer to the Question is option a ( Only 8 )

Answer 2

Appropriate Question :

⠀⠀⠀⠀━━ Two plane mirrors are inclined at an angle 40⁰ between them. Number of ⠀⠀⠀⠀⠀images seen of a tiny object kept between them is :

⠀⠀⠀⠀1). Only 8 ⠀⠀✔

⠀⠀⠀⠀2). Only 9

⠀⠀⠀⠀3). 8 or 9

⠀⠀⠀⠀4). 9 or 10

⠀⠀⠀⠀⠀${\underline{ \mathrm {\:\:The\:number \:of\:images \:formed \:is\:\bf{8\:\:[ \:Option\:A \:\:: \:(Only\:8)\:\:].\:\:}}}}$

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Given : Two plane mirrors are inclined at an angle 40⁰ $\bf [\:\theta\:]$ between them .

Exigency To Find : Number of images formed of a tiny object .

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$\dag\:\:\sf{ As,\:We\:know\:that\::}\\\\ \qquad \maltese\:\: \bf Number\:of\:Images\:Formed\::$

$\qquad \dag\:\:\bigg\lgroup \sf{ Number _{(Images \:Formed \:)} \:: \bigg( \dfrac{360}{\theta }\bigg) - 1 }\bigg\rgroup$

⠀⠀⠀⠀⠀Here , $\bf \theta$ is the angle between them & which is 40⁰ .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad :\implies \sf Number _{(Images \:Formed)} \: = \: \bigg( \dfrac{360}{\theta }\bigg) - 1$

$\qquad :\implies \sf Number _{(Images \:Formed)} \: = \: \bigg( \dfrac{360}{40 }\bigg) - 1$

$\qquad :\implies \sf Number _{(Images \:Formed)} \: = \: \bigg(\cancel {\dfrac{360}{40 }}\bigg) - 1 \qquad \qquad$ [ Canceled by 40 ]

$\qquad :\implies \sf Number _{(Images \:Formed)} \: = \: 9 - 1$

$\qquad :\implies \sf Number _{(Images \:Formed)} \: = \: 8$

$\qquad:\implies \frak{\underline{\purple{\:Number _{(Images \:Formed)} \: = \: 8 }} }\:\:\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Hence,\:The\:number \:of\:images \:formed \:is\:\bf{8}}}}$

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