Artigo sobre a ecuación das lentes diverxentes (cóncavas)
Antes de derivar a ecuación da lente cóncava, primeiro comprendimos as regras dos signos da lente cóncava.
Regras de signos da lente cóncava
As seguintes son as regras de signos da lente cóncava.
- Distancia ao obxecto (do)
Se o obxecto está no lado da lente que coincide coa dirección do feixe de luz, entón a distancia ao obxecto é positiva.
- A distancia da imaxe (di)
If a beam of light passes the image, then a distancia da imaxe is positive (real image). If the image does not pass through the beam of light, a distancia da imaxe é negativo (imaxe virtual).
- A distancia focal (f)
If the focal point of the lens is passed through a beam of light, the focal length of the lens is positive. Conversely, if the lens’s focal point is not passed by light, the lens’s focal length is negative. The focal point of the concave lens is not passed by light, so the focal length of the concave lens is negative.
- The height of the object (ho)
If the object is above the principal axis, the height of the object is signed positive (object is upright). Conversely, if the object is below the principal axis, the height of the object is negative (object is inverted).
- The height of the image (hi)
Se a imaxe está por riba do eixe principal, a altura da imaxe é positiva (a imaxe está en posición vertical). Se a imaxe está por debaixo do eixe principal, a altura da imaxe é negativa (a imaxe está invertida).
- Ampliación da imaxe (m)
If the magnification of image > 1, then the image size is greater than the object size. If the magnification of the image = 1, then the image size is equal to the object size. If the magnification of image < 1, the image size is smaller than the object size.
The equation of the concave lens
Based on the figure below, two beams of light are drawn towards the concave lens, and the concave lens refracts the light beam.
s = do = the object distance, s’ = di = the image distance, h = P P’ = the height of object, h’ = Q Q’ = the height of image, F1 e F2 = the focal point of the concave lens.
O triángulo P'AP é semellante ao triángulo Q'AQ. Polo tanto:
O BF2A triangle is similar to the Q’F2Q triangle, where the distance of AB = the height of the object (h) and the distance of F2A = the focal length (f) of the concave lens. Therefore :
Based on the the the sign rules of the concave lens, this equation can be changed to like the equation of curved mirror,
if the image distance (di) is given a negative sign because the beam of light does not pass the image
and the focal length (f) is also given a negative sign because the focal point of the concave lens is not passed by light (compare with the figure of the image formation above). According to this statement, the equation of the concave lens changes to:
do = distancia ao obxecto, di = distancia á imaxe, f = distancia focal
Ampliación da imaxe (m)
Observa a figura da formación da imaxe de arriba. Os triángulos P'AP e Q'AQ son semellantes, polo que podemos derivar a relación entre a distancia do obxecto e a distancia da imaxe coa altura do obxecto e a altura da imaxe:
Esta ecuación escríbese de novo do seguinte xeito engadindo m:
m = o aumento da imaxe
ho = the object height (positive if it is above the principal axis or the object is upright)
hi = the image height (positive if it is above the principal axis or the image is upright)
do = the object distance (positive if the light beam pass through the object)
di = the image distance (positive if the beam of light pass through the image or image is real)
