In the event that the object is closer to the lens than the focal point, the diagram to determine image size and position is somewhat more complex. In this case the beams must be

projected from where they would have reached the object that radiates them
within the projection the same rules as in a real beam must be followed

In this case it is enough to diagram the same three beams again:

- parallel to the optical axis is refracted by the focus
- via the focus is refracted parallel to the optical axis
- via the origin of the continuous optical axis in a straight line

and the image is obtained in the same way:

(ID 9783)

Correcci n con Lentes

(ID 1864)

In the case of a biconvex lens a beam that reaches the lens

- parallel to the optical axis is refracted by the focus
- via the focus is refracted parallel to the optical axis
- via the origin of the continuous optical axis in a straight line

what in the case of an object at a distance greater than the photo corresponds to:

(ID 1856)

A convex lens is a lens that refracts the parallel beam of light that strikes parallel through its focus:

(ID 1855)

Por similitud de los tri ngulos de los tama os del objeto y la imagen y las posiciones del objeto y foco permite por similitud de tri ngulos mostrar que:

(ID 3347)

For any lens you can draw characteristic beams with which you can similarly show that the sizes of the object and the image are in the same proportion as their distances to the optical element (lens or mirror).

If the object has a size a_o, it is at a distance s_o of the lens, the image is a size a_i and is at a distance s_i, by similarity of the triangles it can be shown that

(ID 3346)

Convex lenses are thinner in their center widening towards the edges.

The light beams that have a parallel impact are scattered as if the light were emitted in the lens focus.

(ID 1854)

Lente Bi-Concavo grueso

(ID 1858)

Lente Bi-Convexo grueso

(ID 1857)

Lente Concavo-Convexo grueso

(ID 1859)

Una caso especial es aquel en que los radios son iguales, o sea R=R_1=R_2. Por ello el foco se calcula de:

(ID 3432)

Lente Convexo-Concavo grueso

(ID 1860)

Los lentes reales tienen un grosor que se debe considerar. Si el lente tiene un indice de refracci n n, un grosor en el centro de d y las curvaturas son R_1 y R_2, el foco f se calcula con

(ID 3348)

Una caso especial es aquel en que los radios son iguales, o sea R=R_1=R_2. Por ello el foco se calcula de:

(ID 3430)

Los lentes reales tienen un grosor que se debe considerar. Si el lente tiene vidrio con indice de refracci n n, un grosor en el centro de d y las curvaturas son R_1 y R_2, se puede calcular el foco f. Para ello basta tomar la ecuaci n del lente bi-convexo e introducir el radios de curvatura R_2 con el signo negativo:

(ID 3350)

Una caso especial es aquel en que los radios son iguales, o sea R=R_1=R_2. Por ello el foco se calcula de:

(ID 3431)

Una caso especial es aquel en que los radios son iguales, o sea R=R_1=R_2. Por ello el foco se calcula de:

(ID 3429)

Los lentes reales tienen un grosor que se debe considerar. Si el lente tiene vidrio con indice de refracci n n, un grosor en el centro de d y las curvaturas son R_1 y R_2, se puede calcular el foco f. Para ello basta tomar la ecuaci n del lente bi-convexo e introducir los radios de curvatura con el signo negativo:

(ID 3349)

Cuando se acoplan dos lentes con sus respectivos focos, el primer lente genera una imagen que funciona como objeto para el segundo lente que a su vez genera una imagen de una imagen:

(ID 9465)

Aqui va el applet ...

(ID 194)

The refractive index of glass can depend on the wavelength or frequency of light. In such cases, the glass is referred to as 'chromatic.' If it does not exhibit this property, it is called 'achromatic.'

The main issue with this property is that the focal point of a lens depends on the color of light. Therefore, an optical lens has the problem that if the eye can focus on one color, it will not be able to simultaneously focus on objects of other colors.

(ID 1626)