Article about Equation of converging (convex) lens
Before learning the equation of the convex lens, understand the sign rules of the convex lens below.
Sign rules of the convex lens
- Nisa tsakanin abu (yi)
If an object is passed through a beam of light, then Nisa tsakanin abu da abu tabbatacce ne.
- Nisa ta hoton (di)
If the beam of light passes the image, then Nisa ta hoton is positive (real image). If the beam of light does not pass through the image, Nisa ta hoton yana da kyau (hoton kama-da-wane).
- Tsawon mai da hankali (f)
When the beam of light passes through the focal point of the lens, the lens’s focal length is positive. Conversely, if the light beam does not pass the focal point of the lens, the focal length of the lens is negative. The focal point of the convex lens is passed through the beam of light. Therefore, the focal length of the convex lens is positive.
- The object height (ho)
If the object is above the principal axis, then the object height is signed positive (object is upright). Conversely, if the object is under the principal axis of the convex lens, the object height is negative (object is inverted).
- The image height (hi)
Idan hoton yana sama da babban ginshiƙi, tsayin hoton yana da kyau (hoton yana tsaye). Idan hoton yana ƙasa da babban ginshiƙi, tsayin hoton yana da kyau (hoton yana juyawa).
- Girman hoto (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 the image is < 1, the image size is smaller than the object size.
The equation of the convex lens
s = do = the object distance, s’ = di = the image distance, ho = P P’ = the object height, hi = Q Q’ = the image height, F1 da F2 = the focal point of the converging lens.
Alwatika na P'AP yayi kama da alwatika na Q'AQ. Saboda haka:
Triangle BF2A = Q'F2Q where the distance of AB = the object height (h) and the distance of F2A = the focal length (f) of the convex lens. Therefore :
do = the object distance (positive if the object is passed through by the light beam)
di = the image distance (positive if the image is passed through by the light beam or image is real)
f = the focal length (positive if the focal point of the convex lens is passed through by the light beam)
Always remember the sign rules of the convex lenses when using this equation to solve the problem of the convex lenses.
Girman hoto (M)
Observe the formation of the image above. Similar to the PAP ‘and QAQ’ triangles, we can derive the relationship between the object distance and the image distance with the object height and the image height:
The equation above can be written again as below by adding the symbol m:
m = girman hoton
ho = the object height (positive if the object is above the principal axis of the convex lens or the object is upright)
hi = the image height (negative if the image is below the principal axis of the convex lens or the image is inverted)
do = the object distance (positive if the object is passed through by the light beam)
di = the image distance (positive if the image is passed through the light beam or the image is real)
