# Divergine Lens Embedded within Converging Lens

• Ryan Rodriguez
In summary, the problem involves a thin converging lens made of glass with an inclusion of water at the center. The lens surfaces have radii of curvature of 10m and the water inclusion has a diverging lens shape with radii of curvature of -20m. A laser beam of 10m diameter is parallel to the optical axis and hits the center of the lens. The position where the laser light gets focused to a point can be found using the lensmaker's equation and the indices of refraction for glass and water. The resulting point is a virtual image, and the diameter of the laser light on a screen placed 20m away can be calculated using the thin lens formula.
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?

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.

## What is a "Diverging Lens Embedded within Converging Lens"?

A "Diverging Lens Embedded within Converging Lens" is a type of lens system where a diverging lens is placed within a converging lens. This creates a unique optical setup that allows for greater control over the direction and focus of light rays passing through the lenses.

## How does a "Diverging Lens Embedded within Converging Lens" work?

The diverging lens in this setup helps to spread out light rays, while the converging lens then focuses those rays to a specific point. This allows for a more precise and controlled manipulation of light, making it useful in applications such as microscopy and photography.

## What are the advantages of using a "Diverging Lens Embedded within Converging Lens"?

One advantage is that it allows for a greater range of control over the direction and focus of light rays, compared to using just a single lens. This can be beneficial in various optical instruments and devices. Additionally, this setup can also help to reduce certain types of optical aberrations.

## What are the limitations of using a "Diverging Lens Embedded within Converging Lens"?

One limitation is that it can be more complex and expensive to produce and use compared to a single lens. Additionally, the placement and alignment of the lenses must be precise for optimal results. This setup may also be limited in its ability to manipulate certain types of light waves, such as polarized light.

## How is a "Diverging Lens Embedded within Converging Lens" different from other lens setups?

This setup is unique in that it combines the properties of both a diverging and a converging lens, allowing for more precise control over light rays. Other lens setups, such as using multiple lenses in a row, may also achieve similar effects but may not be as efficient or effective in manipulating light.

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