# Thread: simple question :/ is my textbook wrong?

1. Hi Everyone I'm new to the forum, and decided to join because a question on physics is playing with my head

"When the sun is directly overhead, a narrow shaft of light enteres a small hole in the ceiling of a room. The ceiling is flat and is 10m above the floor. A bright spot moves across the floor below at the seem of V cm.s^-1."

Q1 is fairly simple - calculate V

v = rw where r is radius and w is angular velocity..
v = 10m * (2*pi / 24 * 60 * 60)
v ~ .073 cm/s.

The second part to the question states:

"The room has a polished floor and the beam of light is reflected onto the roof. At which speed does the dot move on the ceiling?"

- The answer + solution they provide is 2 * V. Because v = rw, and since r is no longer 10m but 20m (the light travels twice as far)..

THIS doesn't make sense to me? woudln't the velocity of the light move across the ceiling at the same speed as the on the floor? i'd understand if the room was 20m from floor to ceiling but this is a reflection?

2.

3. If the reflected spot on the ceiling moved at the same speed as the spot on the floor, it would remain directly above it. But it doesn't, does it?

4. i actually worked it out... i drew a diagram and the text book is right...the beam of light on the ceiling moves at twice the speed as the one on te floor because when the distance from the beam to the hole is x..the distance from the hole to the beam on the ceiling is 2x (because the light reflected is at the same angle as the incident ray...)

thanks though
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