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Two concave mirrors each of focal length 'f' are placed infront of each other co=axially at a distance of 4d in a medium of refractive index n_(0). A plane galss slab of refractive index 'n' & thickness 'd' is placed at a distance of 'd' from M_(1).A point object O is placed at a distace of 'd' from M_(2) as shown in the figure. Consider first reflection by M_(2), then refraction on slab and then reflection by M_(1). Determine the distance of this iamge after reflection from M_(1) |
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Answer» `rArr v_(1)=((-d)(-f))/(-d+f)=(DF)/(f-d)` {`u_(1),v_(1)` coordinates of object `&` image resp. `w.r.t.` pole `S` and POSITIVE axis as `x`} and `v_(2)=v_(1)-d(v_(1)-d(1-(n_(0))/(n))=(dt)/(f-d)-d(1-(n)/(n_(0)))` [`v_(2)` is coordinate of image after refraction by the slab considering origin at `S` and positive direction as `x` axis] and `u_(3)=-(v_(2)+4d) rArr v_(3)=|(u_(3)(-f))/(u_(3)-(-f))|` [`u_(3)=` coordinate of `v_(2)` considering origin at `S'` and positive direction as `x'.v_(3)=` coordinates of image of `u_(3)`, origin at `S'` and positive direction as `x'`] `|((v_(2)+4d)f)/(-v_(2)-4d+_f)| rArr "distance" |((df)/(f-d)-d(1-(n_(0)/(n))+4d)f)/((df)/(d-f)+d(1-(n_(0))/(n))-4d+f)|` 
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