Optics & Light: Calculating Radius of Curvature

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Homework Help Overview

The problem involves optics and light, specifically calculating the radius of curvature of a surface when parallel light enters a transparent medium with a given refractive index and focuses at a certain distance behind the surface.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the meaning of the focus distance and the nature of the surface involved. There are attempts to identify the correct equations for refraction and to clarify the geometry of the situation, including the assumption of a spherical surface.

Discussion Status

Participants are exploring different equations and concepts related to refraction at a single curved surface. Some guidance has been provided regarding the appropriate equations and the nature of the surface, but there is no explicit consensus on the final approach or solution.

Contextual Notes

There is some confusion regarding the interpretation of the problem statement, particularly about the focus distance and the surface's curvature. Participants are working within the constraints of the problem as posed, with references to relevant equations from their textbooks.

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Homework Statement


Parellel light in air enters a transparent medium of refractive index 1.33 and is focussed 35 mm behind the surface.Calculate the radius of curvature of the surface of the medium.


Homework Equations


Can someone help me with this question , i have no idea where to start with since I dun really understand the question where it says the light the is focused 35 behind the surface. Which surface is it talking about?
Do I need to use n1/p + n2/q = (n2-n1)/R?

The Attempt at a Solution

 
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The surface is the interface between the air and the medium. And it must be curved, in order for the parallel light to come to a focus.

I'm not sure about which equation to use.
 
Assuming the surface is spherical, draw a picture of a sphere.
Remember the normal at each point on the surface goes to the centre of the sphere.
Now draw a parallel ray hitting the normal at that point.
Remember snell's law and a bit of similair triangles.
 
Use I use this equation to do it?
1/f = (n-1)(1/R1 - 1/R2)
 
Not quite but I think you are getting there.

That equation has two R's, since it is for a complete lens which has two sides to it (R1 on one side, R2 on the other side). But this problem only involves one surface, between the air and the medium, so there will be just one "R".

Your book should have a discussion (and an equation) for refraction by a single surface of radius R. That is a good place for you to look.
 
oh i get it
n1/p + n2/q = (n2 - n1)/R
Putting p = infinity, q=f
=> n2/f = (n2-n1) /R
R = f(n2-n1)/ n2
R = 35(1.33-1)/1.33 = 8.68mm
 
Looks good. Sorry about not realizing you had the right equation to begin with!
 

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