Optics & Light: Calculating Radius of Curvature

[hayowazzup]

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

 

[Redbelly98]

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.

 

[mgb_phys]

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.

 

[hayowazzup]

Use I use this equation to do it?
1/f = (n-1)(1/R1 - 1/R2)

 

[Redbelly98]

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.

 

[hayowazzup]

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

 

[Redbelly98]

Looks good. Sorry about not realizing you had the right equation to begin with!