(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
Answers
Explanation:
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
⠀⠀⠀⠀⠀\begin{gathered}{\underline{ \mathrm {\:\:The\:number \:of\:images \:formed \:is\:\bf{8\:\:[ \:Option\:A \:\:: \:(Only\:8)\:\:].\:\:}}}}\\\end{gathered}
Thenumberofimagesformedis8[OptionA:(Only8)].
⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀
Given : Two plane mirrors are inclined at an angle 40⁰ \bf [\:\theta\:][θ] between them .
Exigency To Find : Number of images formed of a tiny object .
⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀
\begin{gathered}\dag\:\:\sf{ As,\:We\:know\:that\::}\\\\ \qquad \maltese\:\: \bf Number\:of\:Images\:Formed\:: \\\\\end{gathered}
†As,Weknowthat:
✠NumberofImagesFormed:
\begin{gathered}\qquad \dag\:\:\bigg\lgroup \sf{ Number _{(Images \:Formed \:)} \:: \bigg( \dfrac{360}{\theta }\bigg) - 1 }\bigg\rgroup \\\\\end{gathered}
†
⎩
⎪
⎪
⎪
⎧
Number
(ImagesFormed)
:(
θ
360
)−1
⎭
⎪
⎪
⎪
⎫
⠀⠀⠀⠀⠀Here , \bf \thetaθ is the angle between them & which is 40⁰ .
⠀⠀⠀⠀⠀⠀\begin{gathered}\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\\end{gathered}
⋆NowBySubstitutingtheknownValues:
\begin{gathered}\qquad :\implies \sf Number _{(Images \:Formed)} \: = \: \bigg( \dfrac{360}{\theta }\bigg) - 1 \\ \end{gathered}
:⟹Number
(ImagesFormed)
=(
θ
360
)−1
\begin{gathered}\qquad :\implies \sf Number _{(Images \:Formed)} \: = \: \bigg( \dfrac{360}{40 }\bigg) - 1 \\ \end{gathered}
:⟹Number
(ImagesFormed)
=(
40
360
)−1
\begin{gathered}\qquad :\implies \sf Number _{(Images \:Formed)} \: = \: \bigg(\cancel {\dfrac{360}{40 }}\bigg) - 1 \qquad \qquad \\ \end{gathered}
:⟹Number
(ImagesFormed)
=(
40
360
)−1
[ Canceled by 40 ]
\begin{gathered}\qquad :\implies \sf Number _{(Images \:Formed)} \: = \: 9 - 1 \\ \end{gathered}
:⟹Number
(ImagesFormed)
=9−1
\begin{gathered}\qquad :\implies \sf Number _{(Images \:Formed)} \: = \: 8 \\ \end{gathered}
:⟹Number
(ImagesFormed)
=8
\begin{gathered}\qquad:\implies \frak{\underline{\purple{\:Number _{(Images \:Formed)} \: = \: 8 }} }\:\:\bigstar \\\end{gathered}
:⟹
Number
(ImagesFormed)
=8
★
Therefore,
⠀⠀⠀⠀⠀\begin{gathered}\therefore {\underline{ \mathrm {\:Hence,\:The\:number \:of\:images \:formed \:is\:\bf{8}}}}\\\end{gathered}
∴
Hence,Thenumberofimagesformedis8
⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━