Lensformula

The power of lens is expressed in Diopter which is the inverse of its focal length expressed in metres, i.e. diopter = m-1.

Spectroscopy allows scientists to investigate pathways of energy flow between molecular states, the role of quantum effects in chemical reactions, and the time scales of relaxation processes within complex systems.

Considering the refraction at the spherical surfaces we can derive an equation for the image formation. The basic concept is that the image formed by the first refracting surface acts as a virtual object for the second refracting surface. By applying Gauss Formula which is a geometrical method to describe the behaviour of light, we can write,

Focal length ofconvex lens calculator

Light Conversion has been a pioneer in this field for almost three decades and has recently brought in a complete commercial solution, called Harpia. With its various modules and customisation options, the Harpia spectroscopy system offers a compact and user-friendly solution to meet the diverse needs in the fascinating science of ultrafast spectroscopy.

Light Conversion’s compact Harpia system is able to to meet the diverse needs of ultrafast spectroscopy (Image: Nail Garejev)

Lens maker’s equation gives the relation between the focal length of the lens, the refractive index of its material, and the radii of curvature of its two surfaces.

Let us consider that the lens is placed in air so that the first and second focal lengths designated by P1F1 and P2 F2 respectively are equal, and we take it as f.

It can cover a wide range of time scales, from femtoseconds to milliseconds, depending on the phenomena being studied, and the temporal resolution required to capture the relevant processes.

The power of lens is expressed in Diopter which is the inverse of its focal length expressed in metres, i.e. diopter = m-1.

Femtosecond lasers and wavelength-tunable sources are the toolkits for ultrafast spectroscopy, providing high temporal resolution and a non-invasive nature to study material properties, as well as the ability to unravel complex phenomena and fundamental processes.

Let us consider that the lens is placed in air so that the first and second focal lengths designated by P1F1 and P2 F2 respectively are equal, and we take it as f.

Power of a lens is the measure of the ability of a lens to converge or diverge the rays falling on it. It is defined as the inverse of the focal length of a lens.

Molecular vibrations, electronic transitions, chemical reactions, energy transfer and fluorescence are all examples of processes that can be investigated using spectroscopy. Overall, it allows researchers to uncover the dynamic properties of molecules and materials across a broad range of time scales, aiding our understanding of fundamental processes in chemistry and physics, as well as material characterisation for solar cells or light-emitting diodes (LEDs).

Power of a lens is the measure of the ability of a lens to converge or diverge the rays falling on it. It is defined as the inverse of the focal length of a lens.

Twolenssystemcalculator

Thick lens is a physically large lens whose spherical surfaces are separated by a distance. In other words, it is a lens whose thickness cannot be neglected when compared to its focal length.

Other techniques are therefore necessary if higher temporal resolution is required for faster fluorescence events. Most of these methods are based on nonlinear optical cross-correlation between the fluorescence signal and a much shorter laser pulse. The fluorescence upconversion technique is based on a nonlinear optic method of sum-frequency generation, therefore its temporal resolution is equivalent to the laser pulse duration. A method that can achieve lower temporal resolution and is easier to implement is Kerr gating spectroscopy. In this technique, there is no need to scan wavelength by wavelength as the entire spectrum is captured at once. Fluorescence is good but only contains information about the excited states, whereas interesting things happen in the ground state as well. Therefore, we switch to time-resolved transient absorption spectroscopy.

Lensequationcalculatorwith steps

Consider a thick lens with a thickness d as in the figure above. Let a ray AB coming from infinity, parallel to the axis be refracted along BG. This ray emerges at the second surface along GF2. Here H1P1 and H2P2 are the two principal planes. Principal planes are the plane perpendicular to the principal axis of the lens and passing through its focal point. Let R1 and R2 be the radii of curvature of the first and second surface respectively and n be the refractive index of the lens material.

Consider a thin convex lens XY with an optical center at C. Let the refractive index of the lens n1 and that of the surrounding medium be n0. The centers of curvature of the two refracting surfaces of the lens be C1 and C2 and let the corresponding radii of curvature be R1 and R2 respectively. Consider a point object O placed on the principle axis of the lens.

The first surface XAY forms a real point-image I1. So in the above equation, v can be replaced by v1 and R by R1. Using sign convention, the distances measured to the left of the principal axis is negative. So, here u is negative and the above equation can be rewritten as,

How to calculate focal length ofconvex lens

Convexmirrorcalculator

Since u = ∞, by applying the Gauss Formula which is a geometrical method to describe the behaviour of light, we can write,

From the figure, the light leaving the first surface would form an image I1 if the second surface was absent. With the second surface, I1 becomes a virtual object for the second surface and it forms an image at I, which is the final image. The equation for the final image formation can be written using Gauss formula. Here we take u =v and R=R2, thus we get,

The second surface of the lens refracts the ray along F2 and the final image is formed at F2. So a similar equation for the second surface can be written as,

If we consider the object at infinity, the image will be formed at the principal focus of the lens. So in the above equation, u=∞ and v=f and can be rewritten as,

For a thin lens, the thickness, d of the lens can be neglected when compared to the lengths of the radii of curvature of its two refracting surfaces, and to the distances of the objects and images from it. So we can put d = 0 in the above equation. So the Lens Maker’s Equation for a thin lens becomes,

The second surface of the lens refracts the ray along F2 and the final image is formed at F2. So a similar equation for the second surface can be written as,

Biconvexlens calculator

Greta Bučytė, of Light Conversion's, shares the many advantages femtosecond lasers deliver to the field of ultrafast spectroscopy

Since u = ∞, by applying the Gauss Formula which is a geometrical method to describe the behaviour of light, we can write,

Thin lens are those lens whose thickness can be neglected when compared to the lengths of the radii of curvature of its two refracting surfaces, and to the distances of the objects and images from it.

Lens maker’s equation gives the relation between the focal length of the lens, the refractive index of its material, and the radii of curvature of its two surfaces.

Several spectroscopic techniques are available to observe molecular processes. For instance, time-resolved fluorescence spectroscopy carries information on molecular processes in excited states, as well as their decay.​ There are a few time-resolved fluorescence spectroscopy techniques such as time-correlated single photon counting (TCSPC), fluorescence upconversion (FU), and Kerr gating. TCSPC enables fluorescence and phosphorescence lifetime measurements by measuring the arrival times of individual photons. TCSPC temporal resolution is limited by the detector response time in order of tens or hundreds of picoseconds, and the acquisition speed is determined by the repetition rate of the laser.

The power of lens is expressed in Diopter which is the inverse of its focal length expressed in metres, i.e. diopter = m-1.

Convex lens calculatorwith steps

Lens maker’s equation gives the relation between the focal length of the lens, the refractive index of its material, and the radii of curvature of its two surfaces.

Transient absorption spectroscopy utilises short laser pulses that can be as short as tens of femtoseconds. These pulses can effectively ‘freeze’ the motion of molecules or materials at specific times during a reaction or a dynamic process. By varying the time delay between the pump and probe pulses, scientists can capture snapshots of the molecular system at various stages of its evolution, providing insights into the underlying dynamics. For this purpose, nanosecond or femtosecond transient absorption techniques can be used. The choice of spectroscopy technique depends on the specific research question, experimental requirements, and the timescales involved. Here are some of many reasons why femtosecond lasers are advantageous:

Power of a lens is the measure of the ability of a lens to converge or diverge the rays falling on it. It is defined as the inverse of the focal length of a lens.

Consider a thick lens with a thickness d as in the figure above. Let a ray AB coming from infinity, parallel to the axis be refracted along BG. This ray emerges at the second surface along GF2. Here H1P1 and H2P2 are the two principal planes. Principal planes are the plane perpendicular to the principal axis of the lens and passing through its focal point. Let R1 and R2 be the radii of curvature of the first and second surface respectively and n be the refractive index of the lens material.

A ray of light OA strikes the first surface at A and is refracted in a direction BI1. This ray is further refracted by the second surface in the direction BI and meets the ray which passes undeviated through the principal axis at I. So, the final image is formed at I after the refraction by the two surfaces of the lens.

Thin lens are those lenses whose thickness can be neglected when compared to the lengths of the radii of curvature of its two refracting surfaces, and to the distances of the objects and images from it.