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A point object is kept at a distance of 2 m from origin on X- axis. A quarter cylinder of radius R=30 cm and refractive index $μ = 1.5$ having its axis $⊥$ to plane of paper is placed between the object and the parabolic reflector at a distance of 130 cm from origin as shown in figure. The position of the image after reflection from the parabolic reflector $y^{2} = 2 x$ is

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$25 c m$

$50 c m$

$100 c m$

$150 c m$

answer is B.

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Detailed Solution

After refraction through the quarter cylinder the emergent ray falls on the parabolic reflector parallel to x-axis.

$\tan (π - θ) = - \frac{1}{{\frac{d y}{d x} |}_{(x_{2}, x_{1})}} = y_{1} \tan 2 θ = \frac{2 \tan θ}{1 - \tan^{2} θ} = \frac{y_{1}}{x_{2} - x_{1}} \Rightarrow x_{2} = \frac{1}{2} m = 50 c m$

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