Why is the following situation impossible? The perpendicular distance of a light

Question

Why is the following situation impossible? The perpendicular
distance of a lightbulb from a large plane mirror is twice
the perpendicular distance of a person from the mirror.
Light from the lightbulb reaches the person by two paths:
(1) it travels to the mirror and reflects from the mirror to
the person, and (2) it travels directly to the person without
reflecting off the mirror. The total distance traveled by the
light in the first case is 3.10 times the distance traveled by
the light in the second case.

Explanation / Answer

let the distance between mirror and person is d

and mirror and bulb is 2d, hnce betwen person and bulb is d

speed of light is c

time taken by the light to reach directly to person t1 = d/c

time taken by the light by relectling by the mirror and reach to person t2 = (2d + d)/c = 3d/c

hence t2 = 3t1, not 3.10 times.

hence above situation is not possible

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