Features

• Material: N-BK7
• Wavelength Range: 350 nm - 2.0 μm (Uncoated)
• Available Uncoated or With One of Three Broadband Antireflection Coating
• Offers Excellent Transmittance Throughout the Visible and Near Infrared
• Focal Lengths Available from 10 to 1000 mm

These uncoated Plano-Convex Lenses are fabricated from RoHS-compliant BK7 glass (N-BK7). N-BK7 is probably the most common optical glass used for high quality optical components. It 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.

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 abberation, 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),

where n is the index of refraction and R is the radius of curvature of the lens surface. These lenses are fabricated from N-BK7, which has an Abbe Number of 64.17.

Although uncoated lenses are highlighted on this page, these N-BK7 Plano-Convex lenses are also available with one of three Antireflection Coatings (-A, -B, or -C), which can reduce the amount of light reflected from each surface of the lens. Links to each of these pages can be found in the table above. Please see theGraphs tab for coating information.

N-BK7 lens kits are also available. Please click here for information.

Below is the transmission curve for N-BK7, a RoHS-compliant form of BK7. Total Transmission is shown for a 10 mm thick, uncoated sample and includes surface reflections. Each N-BK7 plano-convex lenses can be ordered uncoated or with one of the following broadband AR coatings: 350-700 nm (Designated with -A), 650-1050 nm (Designated as -B), or 1050-1620 nm (Designated as -C).

These high-performance multilayer AR coatings have an average reflectance of less than 0.5% (per surface) across the specified wavelength ranges. These coatings are designed for angles of incidence between 0 and 30 degrees (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; these coatings are 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 reflectivity plots.

Click Here for Raw Data
Click to Enlarge

Click on the image to download the raw 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, n_l 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 Specs tab as well as on the mechanical drawing for each lens. 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) principle plane (H") and the position at which a collimated beam incident on the curved surface of the plano-convex is focused. The principle plane positions of a thick lens can be calculated with the following equations:

and

However, as with the thick lens equation, H' simplifies to zero and H" simplifies to

when used to calculate the principle plane locations of plano-convex lenses. f_b is the back focal length of the lens, which is often referred to as the working distance of the lens.