Divergine Lens Embedded within Converging Lens

[Ryan Rodriguez]

Homework Statement

A thin converging lens made of glass ($n_g=1.55$) happens to have an inclusion of water ($n_w=1.33$) at the center. The lens surfaces have radii of curvature $R_{out} = r_1=r_2=10m$, and the water inclusion has the shape of a diverging lens with radii of curvature $R_{in}=r_1=r_2=-20m$. The optical axis of the water inclusion is the same as the optical axis of the glass lens. A laser beam of 10m diameter hits the center of the lens from the left, parallel to the optical axis. Assume that the diameters of the lens and water inclusion are (much) greater than 10mm. (a) Find the position along the optical, where the laser light gets focused to a point. Find its position as a function of symbols $n_g, n_w, R_{out}, R_{in}$ (b) is the point calculated in (a) a real image/focus or a virtual image/focus? (c) A screen is placed perpendicular to the optical axis at distance 20m away from the lens. Find the diameter of the laser light when it hits this screen.

Homework Equations

$\frac{1}{f}=(n-1)(\frac{1}{R_1}+\frac{1}{R_2})$

The Attempt at a Solution

I'm at a bit of a loss as to how to get started with this one. I'm confident that I could get (b) and (c) after I figure out (a), so I'm hoping someone can point me in the right direction? I.e, how do I deal with the embedded diverging lens?

 

[BvU]

Hello Ryan, welcome to PF !

There is something special about PF you need to know: the guidelines require a little more from you than "don't know how to start" as an attempt at solution.

Let me help you to get going, though: You have three indices of refraction (1, 1.55 and 1.33) and your lensmaker's equation only has two (1 and n).

If I were you, I would look at the derivation of the equation to see how to deal with that. And I would make a drawing.