A point object is kept at a distance of 2m from a parabolic reflecting surface y 2 = 2 x . An equiconvex lens is kept at a distance of 1.80 m from the parabolic surface. The focal length of the lens i

Question

A point object is kept at a distance of 2m from a parabolic reflecting surface y 2 = 2 x . 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. Position from origin of the image (in cm), just after reflection (image of mirror) from the surface is 10 x. Find the value of x.

TestHub · Accepted Answer

The object is 2 m from the mirror and the lens is 1.80 m from it, so the object sits at the lens focus (20 cm): the lens sends a parallel beam to the mirror.

For $y^{2} = 2 x = 4 f x$ , $f = 0.5$ m; a parallel beam focuses at the mirror focus, 50 cm from the surface.

$10 x = 50$ gives $x = 5$ . Answer: 5.

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