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Mounted N-BK7 Plano-Convex Lenses (Uncoated)
These uncoated Plano-Convex Lenses are fabricated from RoHS-compliant N-BK7. N-BK7 is typically chosen whenever the additional benefits of UV fused silica (i.e., good transmission further into the UV and a lower coefficient of thermal expansion) are not necessary. These Ø1/2", Ø1", and Ø2" lenses are mounted in SM05 (0.535"-40), SM1 (1.035"-40), and SM2 (2.035"-40) compatible mounts, respectively, for compatibility with our line of SM-threaded lens tubes. Each lens tube is engraved with the item #, lens type, focal length, and an arrow pointing toward the curved surface of the lens.
Like all plano-convex lenses, these lenses have a positive focal length and near-best-form shape for infinite and finite conjugate applications. They can be employed to converge collimated beams or collimate light from a point source. To minimize the introduction of spherical aberration, a collimated light source should be incident on the curved surface of the lens when being focused and a point light source should be incident on the planar surface when being collimated.
The focal length of each lens can be calculated using a simplified thick lens equation:
f = R/(n-1),
Here n is the index of refraction and R is the radius of curvature of the lens surface. For more information, please see the Tutorial tab.
Although uncoated lenses are highlighted on this page, these N-BK7 plano-convex lenses are also available with one of three antireflective coatings (-A, -B, or -C), which reduce the amount of light reflected from each surface of the lens over the specified wavelength range. Links to each of these pages can be found in the selection guide table below. Please see the Graphs tab for coating information.
The transmission graph below is for uncoated N-BK7. It represents total transmission through a 10 mm thick, uncoated sample, and the losses within the 350 nm to 2.0 µm wavelength range are primarily due to surface reflections.
The lenses sold on this page are also available with broadband antireflective coatings, the reflectance traces of which are shown in the graph below.
These high-performance multilayer AR coatings have an average reflectance of less than 0.5% (per surface) across the specified wavelength ranges (except for the -D coating, which provides <1.0% average reflectance) and provide good performance for angles of incidence (AOI) between 0° and 30° (0.5 NA). For optics intended to be used at large incident angles, consider using a custom coating optimized at a 45° angle of incidence; this coating is effective from 25° to 52°. The plot shown below indicates the performance of the standard coatings in this family as a function of wavelength. Broadband coatings have a typical absorption of 0.25%, which is not shown in the reflectance plots.
Click here for detailed substrate data.
In the thick lens equation, use the index of refraction for N-BK7 at the wavelength of interest to approximate the wavelength-dependent focal length of any of the plano-convex lenses.
The focal length of a thick spherical lens can be calculated using the thick lens equation below. In this expression, nl is the index of refraction of the lens, R1 and R2 are the radii of curvature for surfaces 1 and 2, respectively, and d is the center thickness of the lens.
When using the thick lens equation to calculate the focal length of a plano-convex lens, R1=∞ and R2=-R. Note that the minus sign in front of R is due to the sign convention used when deriving the thick lens equations and values of R are reported in the specification tables below. Therefore, via substitution, the thick lens equation becomes:
The focal length of the lens calculated using the simplified thick lens equation directly above is the distance between the second (back) principal plane (H") and the position at which a collimated beam incident on the curved surface of the plano-convex is focused. The principal plane positions of a thick lens can be calculated with the following equations:
However, as with the thick lens equation, H' simplifies to zero and H" simplifies to:
when used to calculate the principal plane locations of plano-convex lenses. fb is the back focal length of the unmounted lens, which is often referred to as the working distance. For mounted lenses, the working distance is measured from the back of the threaded housing.