What Is the Radius of Curvature in Optical Applications?

In summary, the radius of curvature is a measure of how much a curve deviates from being a straight line at any given point. It can be calculated using the formula R = [(1 + (dy/dx)^2)^(3/2)] / (d^2y/dx^2), and is important in science for describing the shape of curves, analyzing motion, and determining forces. It is the inverse of curvature, with a smaller radius indicating a higher degree of curvature. The radius of curvature can also be negative if the curve is concave downwards.
  • #1
miltzi
3
0
What exactly is the radius of curvature of an object? And how would this be applied to a question such as the following:

A glass porthole of a submerged craft has parallel curved sides, both of radius of curvature R. What would R be in order that an object in the water 2m away from the porthole should appear undisplaced to an observer inside the craft? Refractive index of water: 4/3, glass: 3/2, air: 1
 
Physics news on Phys.org
  • #2
Does this help:http://en.wikipedia.org/wiki/Radius_of_curvature_(optics )

Basically its the radius of the circle the curve of the surface would make.
 
Last edited by a moderator:

What is the radius of curvature?

The radius of curvature is a measure of how much a curve deviates from being a straight line at any given point. It is defined as the radius of the circle that best fits the curve at that point.

How do you calculate the radius of curvature?

The radius of curvature can be calculated using the formula: R = [(1 + (dy/dx)^2)^(3/2)] / (d^2y/dx^2), where dy/dx is the first derivative of the curve and d^2y/dx^2 is the second derivative.

Why is the radius of curvature important in science?

The radius of curvature is important in science because it is used to describe the shape of curves and surfaces in various fields such as physics, engineering, and mathematics. It can also be used to analyze the motion of objects and determine the forces acting on them.

How does the radius of curvature relate to curvature?

The radius of curvature is the inverse of curvature. This means that a smaller radius of curvature indicates a higher degree of curvature, while a larger radius of curvature indicates a lower degree of curvature.

Can the radius of curvature be negative?

Yes, the radius of curvature can be negative if the curve is concave downwards. In this case, the curvature is also negative and the radius of curvature is measured from the concave side of the curve.

Similar threads

I Why is Cherenkov radiation blue? And what about refractive index?
    • Classical Physics
Replies
3
Views
804
B Calc Excess Rad on Earth in Curved 3D Space | Feynman Lectures 6-2
    • Special and General Relativity
Replies
29
Views
1K
Find the refractive index for the lens and find the image distance
    • Introductory Physics Homework Help
Replies
3
Views
1K
Calculate the focal distance of the duplicate
    • Introductory Physics Homework Help
Replies
3
Views
822
Light incident on a sphere, focused at a distance ##2R##
    • Introductory Physics Homework Help
Replies
2
Views
855
I Pentaprism with magnification, which surface is curved?
    • Optics
Replies
2
Views
901
Optics. A laser beam is refracted in a piece of glass.
    • Introductory Physics Homework Help
Replies
1
Views
975
B Problems I Have With Electrostatics and Pith Ball Experiments
    • Classical Physics
Replies
10
Views
2K
Radius of Curvature to Correct Myopia
    • Introductory Physics Homework Help
Replies
3
Views
2K
What is the internal radius of the optical fibre
    • Introductory Physics Homework Help
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top