At what angle to the surface must a submerged diver in a lake look toward the surface to see the setting sun just along the horizon?
Let A be the required angle to the VERTICAL.
Snell's law says that, in this case,
N sin A = 1*sin 90 = 1
sin A = 1/N = 0.75
A = 48.6 degrees
where N is the refractive index of water.
The angle they want is 90 - A
1sin(theta)=1.33sin (45)
(Theta)=sin^-1 (0.940452019)
therefore Theta= 19.87
1sin(theta)=1.33sin (45)
(Theta)=sin^-1 (0.940452019)
therefore Theta=19.87 degrees
To determine at what angle to the surface a submerged diver must look toward the setting sun just along the horizon, we can use the concept of the critical angle.
The critical angle is the angle of incidence at which light traveling from a denser medium to a less dense medium refracts so much that it travels parallel to the boundary between the two mediums. In this case, the boundary between the water and air acts as the interface.
To calculate the critical angle, we need to know the refractive index of water and air. The refractive index of water is approximately 1.33, and the refractive index of air is approximately 1.00.
The formula to calculate the critical angle is:
Critical angle = arcsin(n2/n1)
where n1 is the refractive index of the medium the light is coming from (water in this case) and n2 is the refractive index of the medium the light is entering (air in this case).
Using the given values, we can calculate:
Critical angle = arcsin(1.00/1.33)
Using a scientific calculator or an online trigonometric calculator, the critical angle is approximately 48.8 degrees.
Therefore, the submerged diver must look at an angle of approximately 48.8 degrees to the surface to see the setting sun just along the horizon.