A submerged scuba diver looks up towards the calm water of a lake and notes that the Sun appears to be 20 from the vertical. The diver's friend, standing on the shore of the lake, is also looking at the Sun.
At what angle from the vertical does the diver's friend see the Sun ? Assume the refractive index of water is 1.33.
Give your answer in degrees.
If the scuba diver is looking from the water n=1.33 and the other man is above water so n=1, use the equation n1sin(theta)=n2sin(theta).
1.33sin(20)=1sin(theta)
27.06 degrees is the answer, but since it says from the horizontal do 90-27.06
An object with a height of 33 cm is placed 2.0 m in front of a convex mirror with a focal length of 75m. (a) Determine the approximate location and size of the image using a ray
diagram. (b) Is the image upright or inverted?
To find the angle from the vertical at which the diver's friend sees the Sun, we can use the concept of refraction.
The apparent angle of the Sun when observed from the water is 20 degrees from the vertical. This means that the light rays from the Sun are bending as they pass from air into water.
We can use Snell's law to determine the angle at which the light rays enter the water. Snell's law states:
n₁*sin(θ₁) = n₂*sin(θ₂),
where n₁ and n₂ are the refractive indices of the initial and final mediums, and θ₁ and θ₂ are the angles of incidence and refraction, respectively.
In this case, the refractive index of air is approximately 1 (since it's close to vacuum) and the refractive index of water is given as 1.33. We'll let θ₁ be the angle between the Sun and the normal (vertical line) when observed in air, and θ₂ be the angle between the Sun and the normal when observed in water.
We can set up the equation as follows:
1*sin(θ₁) = 1.33*sin(θ₂).
Rearranging the equation, we find:
θ₂ = arcsin((1*sin(θ₁))/1.33).
Plugging in θ₁ = 20 degrees:
θ₂ = arcsin((1*sin(20))/1.33) ≈ 14.92 degrees.
Therefore, the diver's friend sees the Sun at an angle of approximately 14.92 degrees from the vertical.
To find the angle at which the diver's friend sees the Sun, we can use Snell's law, which relates the angle of incidence and refraction of light as it passes from one medium to another.
First, we need to determine the angle of incidence for the diver. The angle between the vertical and the Sun, as observed by the diver, is given as 20 degrees.
We can use Snell's law:
n1 * sin(theta1) = n2 * sin(theta2)
Where:
n1 is the refractive index of the initial medium (air) = 1 (approximated)
n2 is the refractive index of the final medium (water) = 1.33 (given)
theta1 is the angle of incidence in the initial medium (diver's observation angle)
theta2 is the angle of refraction in the final medium (unknown)
We can rearrange the equation to solve for theta2:
theta2 = sin^(-1)((n1 / n2) * sin(theta1))
theta2 = sin^(-1)((1 / 1.33) * sin(20))
theta2 ≈ 14.48 degrees
Therefore, the diver's friend sees the Sun at an angle of approximately 14.48 degrees from the vertical.