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An object $M$ is placed at a distance of 3 $m$ from a mirror with its lower end at 2 $m$ from ground as shown in figure below. There is a person at a distance of 4 $m$ from object. Find minimum and maximum height of person to see the image of object?

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a

$h_{m i n} = \frac{20}{3} m, h_{m a x} = \frac{40}{3} m$

b

$h_{m i n} = \frac{25}{3} m, h_{m a x} = \frac{40}{3} m$

c

$h_{m i n} = \frac{20}{3} m, h_{m a x} = \frac{47}{3} m$

d

$h_{m i n} = \frac{25}{3} m, h_{m a x} = \frac{47}{3} m$

answer is A.

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Detailed Solution

From the question,

Question Image

$\frac{h_{m i n}}{10} = \frac{2}{3} ∴ h_{m i n} = \frac{20}{3} m$

$\frac{h_{m a x}}{10} = \frac{4}{3} ∴ h_{m a x} = \frac{40}{3} m$

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An object M is placed at a distance of 3mfrom a mirror with its lower end at 2m from ground as shown in figure below. There is a person at a distance of 4m from object. Find minimum and maximum height of person to see the image of object?