A crown glass plate 2.5 cm thick is placed over a newspaper. How far beneath the top surface of the plate would the print appear to be if you were looking almost vertically downward through the plate?

To determine the apparent position of the print beneath the top surface of the glass plate, we need to consider the phenomenon of refraction.

Refraction occurs when light passes from one medium to another, such as from air to glass. It causes the light to change direction, and this change in direction is dependent on the properties of the media involved.

In this case, the light travels from air to the glass plate, through the plate, and then back into the air again. To calculate the apparent position of the print, we can use Snell's law, which relates the angles of incidence and refraction for a ray of light passing through different media.

Snell's law can be expressed as:

n1 * sin(θ1) = n2 * sin(θ2)

Where:
n1 and n2 are the indices of refraction of the two media (air and crown glass, respectively)
θ1 is the angle of incidence (the angle of the incoming light ray with respect to the normal to the surface of the glass)
θ2 is the angle of refraction (the angle of the light ray with respect to the normal inside the glass)

In this case, we are looking almost vertically downward through the plate, so the angle of incidence is close to 90 degrees, making sin(θ1) ≈ 1.

Now, the index of refraction for crown glass is around 1.52, and we can assume the index of refraction for air is approximately 1.

Using Snell's law, we can rewrite the equation as:

1 * sin(θ1) = 1.52 * sin(θ2)

Since sin(θ1) ≈ 1, we can simplify the equation to:

1 = 1.52 * sin(θ2)

Rearranging the equation, we find:

sin(θ2) = 1 / 1.52

Taking the inverse sine (sin^-1) of both sides, we can determine the value of θ2, which represents the angle of refraction inside the glass plate.

Now that we have θ2, we can use basic trigonometry to find the distance beneath the top surface of the glass plate at which the print appears.

By multiplying the thickness of the glass plate (2.5 cm) by tan(θ2), we can determine the distance.

Therefore, the formula to calculate the distance is:

Distance = thickness of glass plate * tan(θ2)

By substituting the values into the above formula, we can find the answer to the question.

To determine how far beneath the top surface the print would appear to be when looking almost vertically downward through the plate, we need to consider the refraction of light as it passes through the glass plate.

The key concept to understand is Snell's Law, which relates the angles of incidence and refraction of light as it passes through different media. The formula for Snell's Law is:

n1 * sinθ1 = n2 * sinθ2

Where:
- n1 is the refractive index of the medium the light is coming from (in this case, air)
- θ1 is the angle of incidence
- n2 is the refractive index of the medium the light is entering (in this case, crown glass)
- θ2 is the angle of refraction

In this scenario, we are looking almost vertically downward through the glass plate. This means the angle of incidence (θ1) is very close to 90 degrees, and we can assume sinθ1 is approximately equal to 1. Therefore, Snell's Law simplifies to:

n1 = n2 * sinθ2

To calculate the apparent depth of the print, we need to find the refractive index of crown glass and the angle of refraction.

The refractive index of crown glass is typically around 1.52.

Assuming we are looking straight down (θ2 = 0), we can find the apparent depth using the formula:

apparent depth = real depth / refractive index

Given that the crown glass plate is 2.5 cm thick, the apparent depth can be calculated as follows:

apparent depth = 2.5 cm / 1.52 ≈ 1.64 cm

Therefore, the print would appear to be approximately 1.64 cm beneath the top surface of the glass plate when looking almost vertically downward.