Lens/Radius of Curvature Question

[johnwalton84]

I'm working through some questions on lenses, and I'm a bit stuck on this one involving radius of curvature.

The part of the question I'm having difficulty with is

The lens is made of crown glass of refractive index n=1.51. The radii of both surfaces is the same. What is the radius of curvature of the surfaces?

The lens is bi-convex ([tex]f=+20cm[/tex]). The first part of the question involves finding heights, natures and magnifications of objects which is fine, but this part doesn't make any sense. I thought about using the Lens' Maker's equation but if [tex]R_1=R_2[/tex] would the right-hand-side of this equation not equal zero?

 

[Doc Al]

sign convention

I thought about using the Lens' Maker's equation but if [tex]R_1=R_2[/tex] would the right-hand-side of this equation not equal zero?

No. The usual form of the lens maker's equation assumes a sign convention such that if the center of curvature is on the right side of the lens surface then the radius is positive. Thus [itex]R_1[/itex] is positive, but [itex]R_2[/itex] is negative.

 

[johnwalton84]

I see, thanks

 

[johnwalton84]

Having said that, there's another part to that same question that I'm not sure of. It says

A flint glass lens is placed in contact with the crown glass lens. The refractive index of the flint glass is 1.632 for blue light and 1.615 for red light. What is the focal length of the flint glass lens that would compensate for the chromatic aberration of the crown glass lens?

and I'm not sure where to go with it...

 

[Doc Al]

achromatic doublet

Look up "achromatic doublet": Two lenses (of different dispersive powers) used together to correct chromatic dispersion. The basic idea is to create a composite lens that focuses the red and blue light at the same point.