1) How much longer would it take for light to travel through 1.0 km of water than 1.0 km of air?
What formula do you use? The answer is 1.1 x 10^-6 s
2) The acetate roll on overhead projector is placed at a distance 1.2f from the lens. (where f is the focal length). At what distance should the screen be placed to properly focus the image?
Why is the answer 6f?
1
c /v(water) = n - refractive index (for water n=1.33)
v =c/n = 3•10^8/1.33=2.26•10^8 m/s
t1=s/c=1000/3•10^8=3.3•10^-6 s.
t2=s/v=1000/2.26•10^8=4.4 •10^-6 s.
t2-t1 =(4.4 -3.3) •10^-6 = 1.1•10^-6 s
2
1/f=1/di+1/do
di=f•do/(do-f) =
=f•1.2f/(1.2f-f)=
=1.2f²/0.2f = 6f
1) To calculate how much longer it would take for light to travel through 1.0 km of water compared to 1.0 km of air, we can use the formula:
Δt = (d / c)
where Δt is the time taken for light to travel, d is the distance traveled, and c is the speed of light in the medium.
The speed of light in air is approximately 3.0 x 10^8 m/s, and in water, it is approximately 2.25 x 10^8 m/s. Therefore, we can plug these values into the formula:
Δt (water) = (1.0 km / 2.25 x 10^8 m/s) = 4.44 x 10^-6 s
Δt (air) = (1.0 km / 3.0 x 10^8 m/s) = 3.33 x 10^-6 s
The difference between the two times is:
Δt (water) - Δt (air) = (4.44 x 10^-6 s) - (3.33 x 10^-6 s)
= 1.11 x 10^-6 s
Therefore, the answer is approximately 1.1 x 10^-6 s.
2) When the acetate roll on the overhead projector is placed at a distance 1.2f from the lens, the image formed by the lens is at the same distance on the other side. This distance is known as the focal length (f).
To properly focus the image on a screen, the screen should be placed at a distance equal to six times the focal length (6f). This is because, for a lens, the distance at which the image is formed depends on the distance between the object and the lens, as well as the focal length.
The specific reason why the answer is 6f is based on the lens equation:
1/f = 1/di - 1/do
In this equation, f is the focal length, di is the image distance, and do is the object distance. When the object distance (do) is very large compared to the focal length (f), as in the case of an overhead projector, the equation simplifies to:
1/f = 1/di
This means that the image distance (di) is equal to the focal length (f). Placing the screen at a distance equal to six times the focal length (6f) allows for proper focusing of the image.
1) To find out how much longer it would take for light to travel through 1.0 km of water compared to 1.0 km of air, we can use the formula for calculating the time it takes for light to travel through a medium:
t = d / c
where:
t is the time it takes for light to travel through the medium,
d is the distance the light travels, and
c is the speed of light in that medium.
For air, the speed of light is approximately 3.00 x 10^8 meters per second (m/s).
For water, the speed of light is approximately 2.25 x 10^8 m/s.
Let's first convert 1.0 km to meters:
1.0 km = 1000 m
Now we can plug in the values to the formula for air and water:
For air: t_air = (1000 m) / (3.00 x 10^8 m/s) = 3.33 x 10^-6 s
For water: t_water = (1000 m) / (2.25 x 10^8 m/s) = 4.44 x 10^-6 s
The difference between t_water and t_air is:
t_difference = t_water - t_air
t_difference = (4.44 x 10^-6) - (3.33 x 10^-6)
t_difference = 1.1 x 10^-6 s
Therefore, the answer is 1.1 x 10^-6 s, which means it would take 1.1 x 10^-6 seconds longer for light to travel through 1.0 km of water compared to 1.0 km of air.
2) The formula for calculating the distance of an object from the lens in terms of the focal length and the distance of the image from the lens is:
1/f = 1/do + 1/di
where:
f is the focal length of the lens,
do is the distance of the object from the lens, and
di is the distance of the image from the lens.
In this case, the acetate roll on the overhead projector is placed at a distance of 1.2f from the lens. So we can substitute this value for the distance of the object:
do = 1.2f
Now we need to find the distance at which the screen should be placed to properly focus the image. This corresponds to the distance of the image, di.
To find di, we can rearrange the formula:
1/di = 1/f - 1/do
Substituting the values we have:
1/di = 1/f - 1/(1.2f)
Simplifying the equation:
1/di = (1 - 1/1.2)/f
1/di = (1.2 - 1)/1.2f
1/di = 0.2/1.2f
di = (1.2f)/0.2
di = 6f
Therefore, the answer is 6f. The screen should be placed at a distance of 6 times the focal length of the lens to properly focus the image.