1. Input Parameters
2. Calculation Method
Custom lenses are costly. It's often more practical to start with a standard lens focal length and find a suitable detector.
3. Calculated Results
Required Detector Length ($L_D$)
--
mm
Required Focusing Lens ($L_F$)
--
mm
Linear Dispersion
--
nm / mm
Optical Layout Visualization
This diagram illustrates the relationship between the focusing lens, angular span of light, and the detector. It updates as you change the parameters.
Design Principles
The Role of the Focusing Lens and Detector
The focusing lens is a key component in a spectrometer. Its primary function is to focus the dispersed light from the grating onto the detector. The detector, typically a linear array sensor, then measures the intensity of each wavelength. A key design consideration is ensuring that the full range of wavelengths fits precisely onto the physical length of your detector.
Relationship Between Span and Detector Length
The angular span of the dispersed light, δ = βλmax - βλmin, is the difference between the diffraction angles for your maximum and minimum wavelengths. The focusing lens converts this angular span into a linear distance on the detector.
Calculating Focal Length ($L_F$)
The linear dispersion relates the change in position on the detector (dx) to the change in wavelength (dλ). By approximating for the full span, we can derive a practical formula to find either the required detector length or the focal length of the focusing lens:
LF = (LD × d × cos(β)) / (m × (λmax - λmin))