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A point object is kept at a distance of ...

A point object is kept at a distance of `2` m from a parabolic reflecting surface `y^(2) = 2x` . An equiconvex lens is kept at a distance of `1.80` m from the parabolic surface. The focal length of the lens is `20` cm . Find the position from origin of the image in cm, after reflection from the surface.

Text Solution

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Comparing with `y^(2) = 4"ax" implies a = 0.5`
`PC` is a normal so `"tan"(pi-theta) = (-1)/((dy//dx)_(x_(1)y_(1))) = -y_(1) implies ` final position of image = `0.5"m" = 50 "cm"`
But `"tan"2theta = (y_(1)-0)/(x_(2)-x_(1))` & `"tan"2theta = (2"tan"theta)/(1-tan^(2)theta) implies (xy_(1))/(x_(2) - x_(1)) = (2(y_(1)))/(1-y_(1)^(2))x_(2) = (1)/(2)"m"`
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