Question Part
Points
Submissions Used
A flint glass plate (n = 1.66) rests on the bottom of an aquarium tank. The plate is 6.50 cm thick (vertical dimension) and is covered with a layer of water (n = 1.33) 15.0 cm deep. Calculate the apparent thickness of the plate as viewed from straight above the water. (Assume nearly normal incidence.)
To calculate the apparent thickness of the plate as viewed from straight above the water, you need to consider refraction at the air-glass and water-glass interfaces.
Let's break down the problem step by step:
1. Determine the angle of incidence at the air-glass interface.
Since it is assumed to be nearly normal incidence, the angle of incidence (θ1) would be very close to 0 degrees.
2. Calculate the angle of refraction at the air-glass interface.
Using Snell's law:
n1 * sin(θ1) = n2 * sin(θ2)
where n1 is the refractive index of air (approximately 1) and n2 is the refractive index of glass (given as 1.66). Since θ1 is close to 0 degrees, we can approximate sin(θ1) to be 0. Therefore, sin(θ2) = (n1 * sin(θ1)) / n2 = 0.
This means that the light will not be refracted at the air-glass interface since it is nearly perpendicular to the interface.
3. Determine the angle of incidence at the water-glass interface.
The angle of incidence (θ3) is the same as the angle of refraction at the air-glass interface, which is 0 degrees.
4. Calculate the angle of refraction at the water-glass interface.
Using Snell's law:
n3 * sin(θ3) = n2 * sin(θ4)
where n3 is the refractive index of water (given as 1.33) and n2 is the refractive index of glass (given as 1.66). Since θ3 is 0 degrees, sin(θ3) is 0. Therefore, sin(θ4) = (n3 * sin(θ3)) / n2 = 0.
This means that the light will not be refracted at the water-glass interface since it is nearly perpendicular to the interface.
5. Calculate the apparent thickness of the plate.
The total apparent thickness of the plate can be found by summing the thicknesses of the air and water layers above the glass plate. In this case, the apparent thickness will be equal to the actual thickness of the plate, which is given as 6.50 cm.
Therefore, the apparent thickness of the plate as viewed from straight above the water is 6.50 cm.
Remember, Snell's law is fundamental in understanding the refraction of light at interfaces. It 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.