N-BK7 Bi-Convex Spherical Singlets
Lens Shape	Convex/Convex
Material	N-BK7 (Grade A)
Wavelength Range*	350 nm - 2.0 μm (Uncoated)
Design Wavelength	587.6 nm
Index of Refraction	1.515 (@ 633 nm)
Surface Quality	40-20 Scratch-Dig
Surface Irregularity	λ/4
Spherical Surface Power	3λ/2
Abbe Number	v_d=64.17
Centration	≤3 arcmin
Clear Aperture	>90% of Diameter
Diameter Tolerance	+0.00 mm / -0.10 mm
Focal Length Tolerance	±1%

*Also available with a -A coating for the 350-700 nm range, a -B coating for the 650-1050 nm range, or a -C coating for the 1050-1620 nm range.

Bi-Convex Lens Selection Guide
N-BK7	Uncoated -A (350 - 700 nm) -B (650 - 1050 nm) -C (1050 - 1620 nm)
UV Fused Silica	Uncoated -UV (290 - 370 nm) -A (350 - 700 nm) -B (650 - 1050 nm) -C (1050 - 1620 nm)
CaF₂	Uncoated -E (3 - 5 µm)
ZnSe	-F (8 - 12 µm)

Custom Coatings are also available. Please contact our technical support staff for a quote.

Features

Material: N-BK7
Wavelength Range: 350 - 2000 nm (Uncoated)
Available Sizes: Ø6.0 mm, Ø9.0 mm, Ø1/2", Ø1", and Ø2"
Focal Lengths Available from 10.0 mm to 1.0 m
Well Suited for Many Finite Imaging Applications
Offers Excellent Transmittance Throughout the Visible and Near Infrared

Thorlabs' uncoated N-BK7 Bi-Convex Lenses are popular for many finite imaging applications. This type of lens is best suited for use in situations where the object and image are on opposite sides of the lens and the ratio of the image and object distances (conjugate ratio) is between 0.2 and 5. These lenses are designed to have a focal length of f= (R1*R2)/((n-1)*(R2-R1)).

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.

Although this page features our uncoated bi-convex lenses, these lenses are also available with one of three antireflection coatings (-A, -B, or -C) deposited on both sides to reduce the amount of light reflected from each surface. Links to each of these pages can be found in the table to the right. Please see the Graphs tab for coating details.

Lens kits are available. Please click here for information.

Quick Links to Other Spherical Singlets
Plano-Convex	Bi-Convex	Best Form	Plano-Concave	Bi-Concave	Positive Meniscus	Negative Meniscus

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 bi-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

N-BK7 AR Coating Curve

$BK7 Index of Refraction$
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.

thick lens equation

For bi-convex lenses, where the front and back radii of curvature are equal in magnitude and opposite in sign, R₁ = -R₂ = R, we have

Lens Equation Final Biconvex

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 bi-convex is focused. The same analysis can be performed using a point source and the first (front) principle plane (H'). The principle plane positions of a thick lens can be calculated with the following equations:

and

Again, for the same bi-convex lens, R₁ = -R₂ = R, we can solve for H' and H' :

Principle Plane Final

Recommended Mounting Options for Ø6 mm Lenses
Item #	Description
LMR05 with LMRA6	Lens Mount for Ø1/2" Optics with Ø6 mm Optic Adapter
LH1	Adjustable Lens Mount: 0.2" (5 mm) to 1.82" (46 mm)
SCL03	Self-Centering Lens Mount, Ø0.15" (3.8mm) to Ø1.7" (43mm)
SCL04	Self-Centering Lens Mount, Ø0.15" (3.8mm) to Ø3.0" (76mm)
Recommended Mounting Options for Ø9 mm Lenses
LMR05 with LMRA9	Lens Mount for Ø1/2" Optics with Ø9 mm Optic Adapter
LH1	Adjustable Lens Mount: 0.2" (5 mm) to 1.82" (46 mm)
SCL03	Self-Centering Lens Mount, Ø0.15" (3.8mm) to Ø1.7" (43mm)
SCL04	Self-Centering Lens Mount, Ø0.15" (3.8mm) to Ø3.0" (76mm)
Recommended Mounting Options for Ø1/2" (12.7 mm) Lenses
LH1	Adjustable Lens Mount: 0.2" (5 mm) to 1.82" (46 mm)
SCL03	Self-Centering Lens Mount, Ø0.15" (3.8mm) to Ø1.7" (43mm)
SCL04	Self-Centering Lens Mount, Ø0.15" (3.8mm) to Ø3.0" (76mm)
LMR05	Fixed Lens Mount for Ø1/2" Optics
LMR05S	Ø1/2" Lens Mount with Internal and External SM05 Threads
SM05L10	Thorlabs offers a range of Ø1/2" lens tube designs and lengths
LM05XY or LM05XY/M	Translating Lens Mount for Ø1/2" Optics
SCP05	16 mm Cage-System-Compatible XY Translator for Ø1/2" Optics
Recommended Mounting Options for Ø1" (25.4 mm) Lenses
LH1	Adjustable Lens Mount: 0.2" (5 mm) to 1.82" (46 mm)
LH2	Adjustable Lens Mount: 0.75" (19 mm) to 2.25" (57 mm)
SCL03	Self-Centering Lens Mount, Ø0.15" (3.8mm) to Ø1.7" (43mm)
LMR1	Fixed Lens Mount for Ø1" Optics
LMR1S	Ø1" Lens Mount with Internal and External SM1 Threads
SM1L10	Thorlabs offers a range of Ø1" lens tube designs and lengths
LM1XY or LM1XY/M	Translating Lens Mount for Ø1" Optics
HPT1	30 mm Cage-System-Compatible XY Translator for Ø1" Optics
VG100	Adjustable-Height Optic Clamp
Recommended Mounting Options for Ø2" (50.8 mm) Lenses
LH2	Adjustable Lens Mount: 0.75" (19 mm) to 2.25" (57 mm)
SCL04	Self-Centering Lens Mount, Ø0.15" (3.8mm) to Ø3.0" (76mm)
LMR2	Fixed Lens Mount for Ø2" Optics
LMR2S	Ø2" Lens Mount with Internal and External SM2 Threads
SM2L10	Thorlabs offers a range of Ø2" lens tube designs and lengths
LM2XY or LM2XY/M	Translating Lens Mount for Ø2" Optics
VG100	Adjustable-Height Optic Clamp

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Item #

Diameter

Focal Length

Radius of Curvature

Center Thickness

Edge Thickness

Back Focal Length

Reference
Drawing

LB1157

6.0 mm

10.0 mm

9.9 mm

2.4 mm

1.5 mm

9.2 mm

LB1406

6.0 mm

12.0 mm

2.3 mm

1.5 mm

11.2 mm

Item #

Diameter

Focal Length

Radius of Curvature

Center Thickness

Edge Thickness

Back Focal Length

Reference
Drawing

LB1494

9.0 mm

12.0 mm

11.7 mm

3.6 mm

1.8 mm

10.7 mm

LB1212

9.0 mm

20.0 mm

20.1 mm

2.8 mm

1.8 mm

19.0 mm

Item #

Diameter

Focal Length

Radius of Curvature

Center Thickness

Edge Thickness

Back Focal Length

Reference
Drawing

LB1092

1/2"

15.0 mm

14.6 mm

4.7 mm

1.8 mm

13.4 mm

LB1450

1/2"

20.0 mm

19.9 mm

3.9 mm

1.8 mm

18.7 mm

LB1014

1/2"

25.0 mm

25.2 mm

3.4 mm

1.8 mm

23.8 mm

LB1258

1/2"

30.0 mm

30.4 mm

3.1 mm

1.8 mm

28.9 mm

LB1378

1/2"

40.0 mm

40.7 mm

2.8 mm

1.8 mm

39.1 mm

LB1844

1/2"

50.0 mm

51.1 mm

2.6 mm

1.8 mm

49.1 mm

LB1187

1/2"

100.0 mm

102.6 mm

2.2 mm

1.8 mm

99.3 mm

Item #

Diameter

Focal Length

Radius of Curvature

Center Thickness

Edge Thickness

Back Focal Length

Reference
Drawing

LB1761

25.4 mm

24.5 mm

9.0 mm

1.9 mm

22.2 mm

LB1757

30.0 mm

29.5 mm

7.7 mm

2.0 mm

27.3 mm

LB1811

35.0 mm

34.9 mm

6.8 mm

2.0 mm

32.7 mm

LB1027

40.0 mm

40.1 mm

6.1 mm

2.0 mm

37.9 mm

LB1471

50.0 mm

50.6 mm

5.2 mm

2.0 mm

48.2 mm

LB1596

60.0 mm

61.0 mm

4.7 mm

2.0 mm

58.4 mm

LB1901

75.0 mm

76.6 mm

4.1 mm

2.0 mm

73.6 mm

LB1676

100.0 mm

102.4 mm

3.6 mm

2.0 mm

98.8 mm

LB1904

125.0 mm

128.2 mm

3.3 mm

2.0 mm

123.9 mm

LB1437

150.0 mm

154.0 mm

3.1 mm

2.0 mm

149.0 mm

LB1294

175.0 mm

179.8 mm

2.9 mm

2.0 mm

174.0 mm

LB1945

200.0 mm

205.6 mm

2.8 mm

2.0 mm

199.1 mm

LB1056

250.0 mm

257.1 mm

2.6 mm

2.0 mm

249.1 mm

LB1779

300.0 mm

308.6 mm

2.5 mm

2.0 mm

299.2 mm

LB1391

400.0 mm

411.7 mm

2.4 mm

2.0 mm

399.2 mm

LB1869

500.0 mm

514.7 mm

2.3 mm

2.0 mm

499.2 mm

LB1475

750.0 mm

772.2 mm

2.2 mm

2.0 mm

749.3 mm

LB1409

1000.0 mm

1029.8 mm

2.2 mm

2.0 mm

999.3 mm

Item #

Diameter

Focal Length

Radius of Curvature

Center Thickness

Edge Thickness

Back Focal Length

Reference
Drawing

LB1723

60.0 mm

59.3 mm

14.4 mm

3.0 mm

55.0 mm

LB1309

75.0 mm

75.2 mm

11.8 mm

3.0 mm

71.0 mm

LB1630

100.0 mm

101.4 mm

9.5 mm

3.0 mm

96.8 mm

LB1106

125.0 mm

127.4 mm

8.1 mm

3.0 mm

122.3 mm

LB1374

150.0 mm

153.3 mm

7.2 mm

3.0 mm

147.6 mm

LB1607

175.0 mm

179.1 mm

6.6 mm

3.0 mm

172.8 mm

LB1199

200.0 mm

205.0 mm

6.2 mm

3.0 mm

198.0 mm

LB1889

250.0 mm

256.6 mm

5.5 mm

3.0 mm

248.2 mm

LB1917

300.0 mm

308.2 mm

5.1 mm

3.0 mm

298.3 mm

LB1862

400.0 mm

411.3 mm

4.6 mm

3.0 mm

398.5 mm

LB1909

500.0 mm

514.4 mm

4.3 mm

3.0 mm

498.6 mm

LB1247

750.0 mm

772.0 mm

3.8 mm

3.0 mm

748.7 mm

LB1859

1000.0 mm

1029.5 mm

3.6 mm

3.0 mm

998.8 mm

View All »Matching Part Numbers

N-BK7 Bi-Convex Lenses, Uncoated

Features