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Image distance in a spherical mirror + = () Subscripts 1 and 2 refer to initial and final optical media respectively. These ratios are sometimes also used, following simply from other definitions of refractive index, wave phase velocity, and the luminal speed equation:
If an object is located infinitely far away from the system (to the left), then its image made by the system is located at the back focal point. In this case, the 1st lens images the object at its focal point. So, the thin lens formula for the 2nd lens becomes
Distances in the thin lens equation. For a lens of negligible thickness, and focal length f, the distances from the lens to an object, S 1, and from the lens to its image, S 2, are related by the thin lens formula: + =.
The main benefit of using optical power rather than focal length is that the thin lens formula has the object distance, image distance, and focal length all as reciprocals. Additionally, when relatively thin lenses are placed close together their powers approximately add. Thus, a thin 2.0-dioptre lens placed close to a thin 0.5-dioptre lens ...
For a single lens surrounded by a medium of refractive index n = 1, the locations of the principal points H and H ′ with respect to the respective lens vertices are given by the formulas = ′ = (), where f is the focal length of the lens, d is its thickness, and r 1 and r 2 are the radii of curvature of its surfaces. Positive signs indicate ...
The distance between an image and a lens. Real image Virtual image f: The focal length of a lens. Converging lens Diverging lens y o: The height of an object from the optical axis. Erect object Inverted object y i: The height of an image from the optical axis Erect image Inverted image M T: The transverse magnification in imaging (= the ratio ...
A lens with a T-stop of N projects an image of the same brightness as an ideal lens with 100% transmittance and an f-number of N. A particular lens's T-stop, T , is given by dividing the f-number by the square root of the transmittance of that lens: T = N transmittance . {\displaystyle T={\frac {N}{\sqrt {\text{transmittance}}}}.}
A lens with a larger numerical aperture will be able to visualize finer details than a lens with a smaller numerical aperture. Assuming quality (diffraction-limited) optics, lenses with larger numerical apertures collect more light and will generally provide a brighter image, but will provide shallower depth of field.