# Basic optics question - lenses

• jaejoon89
In summary, convex lenses are thicker in the middle and thinner at the edges, causing light rays to converge and form a real image. Concave lenses are thinner in the middle and thicker at the edges, causing light rays to diverge and form a virtual image. The focal length of a lens can be calculated by dividing the radius of curvature of the lens by 2 or by measuring the distance between the lens and the point where light rays converge or diverge. A converging lens is convex and causes light rays to converge, while a diverging lens is concave and causes light rays to diverge. Lenses can form images with all types of electromagnetic radiation, including visible light, infrared, ultraviolet, and even X-rays. They
jaejoon89
Why if two concave and convex lenses are nested together, will there be no resulting convergence or divergence if their focal lengths are the same, but if the concave lens has a larger focal length the rays will converge slightly?

What is (are) the mathematical equation(s)/reason(s)?

Hi jaejoon89!

"Nested" means that the radii of curvature are the same.

So what mathematical equations are involved?

The reason for this is because when two lenses are nested together, their focal lengths act as a combined focal length. This means that the focal length of the resulting lens system will depend on the individual focal lengths of the two lenses. If the two lenses have the same focal length, the resulting focal length will also be the same. This results in no convergence or divergence of the light rays passing through the lenses.

On the other hand, if the concave lens has a larger focal length, the resulting focal length will be longer than the focal length of the convex lens. This means that the light rays passing through the lenses will experience a slight convergence, as the longer focal length of the concave lens will have a stronger effect on the overall focal length of the system.

Mathematically, this can be represented by the lensmaker's equation: 1/f = 1/u + 1/v, where f is the focal length of the lens, u is the object distance, and v is the image distance. When two lenses are nested together, their individual focal lengths can be substituted into this equation to determine the resulting focal length of the system.

In summary, the resulting convergence or divergence of light rays passing through nested lenses depends on the individual focal lengths of the lenses and can be mathematically determined using the lensmaker's equation.

## 1. What is the difference between convex and concave lenses?

Convex lenses are thicker in the middle and thinner at the edges, causing light rays to converge and form a real image. Concave lenses are thinner in the middle and thicker at the edges, causing light rays to diverge and form a virtual image.

## 2. How do you calculate the focal length of a lens?

The focal length of a lens can be calculated by dividing the radius of curvature of the lens by 2. It can also be found by measuring the distance between the lens and the point where light rays converge or diverge.

## 3. What is the difference between a converging lens and a diverging lens?

A converging lens is convex and causes light rays to converge, while a diverging lens is concave and causes light rays to diverge.

## 4. Can lenses only form images with visible light?

No, lenses can form images with all types of electromagnetic radiation, including visible light, infrared, ultraviolet, and even X-rays.

## 5. How do lenses correct vision problems?

Lenses can correct vision problems by altering the path of light rays entering the eye. Convex lenses can correct for farsightedness, while concave lenses can correct for nearsightedness.

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