At the bottom of river there is a lamp. On what minimal distance from the subject its reflection will be placed at the bottom of the river? Refraction index of water is 1.5, depth of the river is 2.5 m.
To find the minimal distance from the subject where its reflection will be placed at the bottom of the river, we need to consider the concept of refraction. Refraction occurs when light passes from one medium to another with a different refractive index.
In this case, we have light traveling from air (refractive index of 1) to water (refractive index of 1.5). The light from the subject will be incident on the surface of the water at some angle, and when it enters the water, it will bend based on the refractive index.
To find the minimal distance, we can use Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two mediums.
Mathematically, Snell's Law is given by: n1 * sin(theta1) = n2 * sin(theta2)
In this case, the light is coming from air with a refractive index of 1 and entering water with a refractive index of 1.5. We need to find the angle of refraction when the light enters the water, and then calculate the distance at which the reflection will be placed at the bottom of the river.
Let's assume the angle of incidence is theta1 and the angle of refraction is theta2.
Since we know the refractive indices and the depth of the river, we can use trigonometry to solve for theta2.
sin(theta2) = (n1 / n2) * sin(theta1)
sin(theta2) = (1 / 1.5) * sin(theta1)
sin(theta2) = (2 / 3) * sin(theta1)
Now, we need to find the distance at which the reflection will be placed at the bottom of the river. This can be calculated using the formula:
distance = depth / tan(angle of refraction)
In this case, the depth of the river is given as 2.5 meters. We need to substitute the calculated value of theta2 into the formula to find the minimal distance.
distance = 2.5 / tan(theta2)
By plugging in the value of theta2, we can find the minimal distance from the subject where its reflection will be placed at the bottom of the river.