Calculating Apparent Depth of Print Beneath Flint Glass Plate

In summary, the print would appear to be 2.1 cm beneath the top surface of the plate if looking almost vertically downward through the plate. This can be determined using the formula Apparent = d/n, where d is the thickness of the plate and n is the refractive index of flint glass (which is 1.66). Drawing a ray diagram and using Snell's law can also provide more confidence in the solution.
  • #1
Aoiumi
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Homework Statement


A flint glass plate 3.5 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?


Homework Equations


N=1.66 for flint glass
Apparent = d/n


The Attempt at a Solution


Apparent depth = 3.5 cm /1.66
= 2.1 cm

I'm not sure if this answer or the formula I used are correct. Thank you.
 
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  • #2
You're right.
You can have more confidence in your solutions, especially in optics, if you draw the ray diagram (using Snell)
One ray travels straight up through the glass "n" into air, undeflected at the surface (sin theta=0).
The other ray goes thru the glass at angle theta_glass from the normal, but deflects as it leaves the glass,
to angle theta_air ... if these angles are small, sin theta ≈ theta.
Using Snell, that means the angle in air is ≈ theta_glass / n.
 
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  • #3
Thank you for your explanation!
 

Related to Calculating Apparent Depth of Print Beneath Flint Glass Plate

1. What is the purpose of calculating apparent depth of print beneath flint glass plate?

The purpose of calculating the apparent depth of print beneath flint glass plate is to determine the true depth of an object when viewed through the glass plate. This calculation takes into account the refractive index of the glass plate and the angle at which the object is viewed, providing a more accurate measurement of the object's depth.

2. How is the apparent depth of print calculated?

The apparent depth of print is calculated using the following formula: apparent depth = actual depth / refractive index. The refractive index of flint glass is typically around 1.5.

3. What is the difference between actual depth and apparent depth?

Actual depth is the true measurement of an object's depth, while apparent depth is the perceived depth when viewed through a medium with a different refractive index. The difference between the two is due to the bending of light as it passes through the medium.

4. What factors can affect the accuracy of the calculated apparent depth?

The accuracy of the calculated apparent depth can be affected by the quality and thickness of the glass plate, the angle at which the object is viewed, and any imperfections in the glass surface.

5. How is the calculated apparent depth used in scientific research?

The calculated apparent depth can be used in various scientific research studies, such as in microscopy and optical measurements. It allows for more accurate measurements of objects and can aid in the understanding of how light behaves when passing through different mediums.

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