Lens and Mirror Calculations and Formulae

The formula for lens makers is as follows:

Where:
    f = Lens focal length
    n = Index of refraction of lens material
    R1 = Radius of curvature of 1st surface
    R2 = Radius of curvature of 2nd surface
    t = Lens thickness

Figure 1 shows a curvature for which R2 is negative.

Shows a curvature for which R2 is negative

Figure 1. Shows a curvature for which R2 is negative

Focal Length of Spherical Mirror

The focal length of a spherical mirror

Figure 2. The focal length of a spherical mirror

The formula for determining the focal length of a spherical mirror (Figure 2) is:

Where r = Radius of curvature of mirror

Effective Focal Length of Two Thin Lenses

Effective focal length of two thin lenses

Figure 4. Effective focal length of two thin lenses

Effective focal length (Figure 3) of two thin lenses can be determined using the following formula:

θ= θ1 + θ2 - θ1 θ2 d

Where:
    f1 = Focal length of lens 1
    f2 = Focal length of lens 2
    θ1 = Power of lens 1
    θ2 = Power of lens 2
    d = Distance between lenses

Image Location and Magnification Formulae, and Graphical Ray Tracing

The Gaussian Lens Formula is as follows:

Magnification is equal to SI/S

Where:
    f = Lens focal length
    S = Object distance
    SI= Image distance

The Newtonian Lens Formula is as follows:

XXI=f2

Magnification is =

The lens formulae and graphical techniques can be used with input and output on the same side of the optic. Ray tracing is shown graphically in Figure 4.

Graphical Ray Tracing

Figure 4. Graphical Ray Tracing

Figure 5 shows the re-imaging of a source using a collimating condenser and refocusing lens.

Re-imaging a source with a collimating condenser and refocusing lens

Figure 5. Re-imaging a source with a collimating condenser and refocusing lens

Focused Spot Size

Uniform illumination of a Diffraction Limited Lens is expressed as follows:

Illumination with a laser beam using a Gaussian intensity profile for a Diffraction Limited Lens is expressed as follows:

About Oriel Instruments

Oriel Instruments, a Newport Corporation brand, was founded in 1969 and quickly gained a reputation as an innovative supplier of products for the making and measuring of light. Today, the Oriel brand represents leading instruments, such as light sources covering a broad range, from UV to IR, pulsed or continuous, and low to high power.

Oriel also offers monochromators and spectrographs, as well as flexible FT-IR spectrometers, which make it easy for users across many industries to build instruments for specific applications. Oriel is also a leader in the area of Photovoltaics with its offering of solar simulators, that allow you to simulate hours of solar radiation in minutes. Oriel continues to bring innovative products and solutions to Newport customers around the world.

This information has been sourced, reviewed and adapted from materials provided by Oriel Instruments.

For more information on this source, please visit Oriel Instruments.

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