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Two concave mirrors each of radius of cu...

Two concave mirrors each of radius of curvature 40cm are placed such that their principal axes are parallel to each other and at a distance of 1cm to each other. Both the mirrors are at a distance of 100cm to each other. Consider first reflection at `M_(1)` and then at `M_(2)` , find the coordinates of the image thus formed. Take location of object as the origin

Text Solution

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Using mirror formula for first reflection:
`1/f=1/v+1/u rArr 1/(-20)=1/v+1/(-60)`
`rArr1/v=1/(60)-1/(20)rArrv=-30cm`
Using mirror formula for second reflection:
`1/f=1/v+1/urArr 1/(-20)=1/v+1/(-70)`
`rArr 1/v=1/(70)-1/(20)=(2-7)/(140)rArrv=-(140)/5=-28cm`
Height of `I_(2)rArrm=((-30)/(-60))=(I_(1))/(-1)rArr I_(1)=1/2cm`
Height of first image from s-axes `=a+1/2=3/2cm`
Height of `I_(2)rArrm=((-28)/(-70))=(2I_2)/3`
=`rArr I_(2)=(3xx28)/(2xx70)I_2=-0.6cm`
Co-ordinate of `I_(2)=(12-0.6)`
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