A meter stick lies on the bottom of a 100 cm long tank with its zero mark against the left edge. You look into the tank at an angle of θ = 30°, with your line of sight just grazing the upper left edge of the tank, and height of the tank is 50cm.
(a) What mark do you see on the meter stick if the tank is empty?
(b) What mark do you see if the tank is half full of water?
(c) What mark do you see if it is completely full of water?
Yo here's how u do it since Kastra aint decide to explain this shi:
1st q simple: use tantheta=y/x, set angle as 30, and 50 cm as y.
2nd question: from the answer from the first q, divide the answer by 2. Keep it with you. Now, for the 2nd half in the water, do n1sintheta1=n2sintheta2 isolate for theta2 (make sure your using the angle as 60 degrees here, if your confused on why search up refraction in water and go to google images, this is the angle you gotta use). Then do the tan(theta)=Y/25 cm, isolate for Y. Then add this answer to the first answer/2.
3rd q: use same angle found from n1sin(theta1)=n2sin(theta2) in q2. Then just do tan(theta)=Y/50 cm, isolate for Y.
Your welcome bozo, and Kastra, you a fraud
Maybe explain how tf to do the question Kastra gah damn
(a) Well, if the tank is empty, you'll see the zero mark on the meter stick. It's not going anywhere!
(b) Now, if the tank is half full of water, things get a bit more interesting. As you look into the tank at that 30° angle, the water will create an apparent shift in the image. The mark you'll see on the meter stick will be around the 50 cm mark, because that's where the water level would be.
(c) When the tank is completely full of water, oh boy, get ready for some optical fun! At that 30° angle, the light will refract through the water, causing some more apparent shifting. You might just see the mark around the 100 cm mark on the meter stick. It's like the water is playing hide-and-seek with you!
Keep in mind, this is all assuming you have keen eyes and a good sense of humor!
To answer these questions, we need to consider the properties of light and the phenomenon of refraction. Refraction occurs when light passes through a medium with a different refractive index, causing the light to change direction. In this case, light passes from air into water, which has a higher refractive index.
(a) When the tank is empty, we can assume that light travels in a straight line from the meter stick to your eye. Since the meter stick is lying on the bottom of the tank, you will see the zero mark on the meter stick. This is because there are no obstructions or refractions to alter the path of the light.
(b) When the tank is half full of water, the light rays will undergo refraction as they pass from air to water. The refracted rays will bend towards the normal, which is an imaginary line perpendicular to the water's surface. As a result, the apparent position of the meter stick will seem higher than it actually is.
To determine what mark you see on the meter stick when the tank is half full, we can use trigonometry. Since the height of the tank is given as 50 cm and the angle of your line of sight is θ = 30°, we can use the tangent function to find the vertical displacement of the mark.
Using the formula tan(θ) = opposite/adjacent, we can rearrange the equation to solve for the opposite side (vertical displacement):
tan(30°) = height of water/adjacent (distance from the left edge to the mark)
tan(30°) = 50 cm/x
x = 50 cm / tan(30°)
x ≈ 86.60 cm
Therefore, if the tank is half full of water, you will see the mark at approximately 86.60 cm on the meter stick.
(c) When the tank is completely full of water, the refraction will be more pronounced. The light rays will again bend towards the normal as they pass from air to water and then from water back to air. This change in direction will cause the apparent position of the meter stick to be even higher than in the previous case.
To determine what mark you see on the meter stick when the tank is completely full, you can apply the same trigonometric approach used in part (b) to find the vertical displacement. However, in this case, the distance from the left edge to the mark will be shorter due to the refraction.
Using the same formula as before, we can solve for x when the height of the water is equal to the height of the tank (50 cm):
tan(30°) = 50 cm/x
x = 50 cm / tan(30°)
x ≈ 86.60 cm
Therefore, if the tank is completely full of water, you will again see the mark at approximately 86.60 cm on the meter stick.
When the tank is empty, you see 86.6 cm.
When the tank is half way full, you see 64.74 cm.
When the tank is full, you see 42.9 cm.