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Q.

Two rays are incident on a spherical mirror of radius R = 5cm. parallel to its optical axis at a distance $h_{1} = 0.5 mm and h_{2} = 3 cm$ from the optic axis. Determine the distance $Δ x$ (approximately) between the points at which these rays intersect the optical axis after being reflected at the mirror.

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a

1.5 cm

b

0.2 cm

c

0.6 cm

d

1.0 cm

answer is C.

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Detailed Solution

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$x = \frac{OD}{\cos α} = \frac{R}{2 \cos α} = \frac{R .R}{2 \sqrt{R^{2} - h^{2}}} = \frac{R^{2}}{2 \sqrt{R^{2} - h^{2}}}$

$∴ x_{1} = \frac{5^{2}}{2 \sqrt{5^{2} - {(0.5)}^{2}}} = 2.525 cm$

$x_{2} = \frac{5^{2}}{2 \sqrt{5^{2} - 3^{2}}} = \frac{25}{2 \times 4} = 3.125 cm$

$Δ x = x_{2} - x_{1} = 3.125 - 2.525$

$= 0.6 cm$

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Two rays are incident on a spherical mirror of radius R = 5cm. parallel to its optical axis at a distance h1=0.5 mm and h2=3 cm from the optic axis. Determine the distance Δx (approximately) between the points at which these rays intersect the optical axis after being reflected at the mirror.