Circular polarization

The magnification of a lens is the ratio of the size of the image to the size of the object. Hence, to find the magnification of a lens, take the ratio of the two. You can also calculate magnification by taking the ratio of the image-lens distance to the object-lens distance.

Degree of polarization

If a beam of linearly polarized monochromatic light enters a birefringent crystal along a direction not parallel to the optical axis of the crystal, the beam will may be divided into two separate beams.  Each will be polarized at right angles to the other, and they will travel in different directions.  The intensity of the original beam will be divided between the two new beams in a manner which depends on the original orientation of the electric field vector with respect to the crystal.  The ratio or the intensities of the two orthogonally polarized beams can have any value.

In other devices the changes in direction of propagation between the two rays is used to separate the incoming beam into two orthogonally polarized beams as in the Wollaston and Thompson beam-splitting prisms.

A half-wave plate δ = π can be used to rotate the plane of linearly polarized light.  The angle of rotation is 2θ, where θ is the angle between the angle of polarization and the wave plate's fast axis.

If we place the object near the lens, we will get its image somewhere. The position, orientation, and size of this image depend on two things: the focal length of the lens (which is specific for the particular lens) and the position of the original object. We can predict what we will see with the following thin lens equation:

Transversewave

There are two basic types of lenses. We can distinguish converging lenses, which have focal length f > 0, and diverging lenses for which focal length f < 0. It should also be noted that when the image distance is positive y > 0, then the image appears on the other side of the lens, and we call it a real image. On the other hand, when y < 0, then the image appears on the same side of the lens as the object, and we call it a virtual image.

When the sun is at a low angle in the sky, the sunlight reflecting off the surface of water is nearly 100% horizontally polarized because the angle of incidence is close to the Brewster angle.  Glare-reducing sunglasses are coated with a polarizer with a vertical transmission axis and therefore block the reflected light.

Remember that magnification must always be a positive number. That's why we have taken the absolute value of y, which generally may be both positive and negative.

Polarization

The figure below shows the trace of the field vector Ex = E0exp(i(kz - ωt)), Ey = E0exp(i(kz - ωt + φ)) in a plane perpendicular to the z-axis when looking towards the source.  (E0x = E0y = E0)

In the Glan-Taylor polarizing prism shown on the right the rejected (ordinary) ray is absorbed by black mounting material in the prism housing.

Circularlypolarizedlight

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The thin lens equation calculator will help you to analyze the optical properties of the simple lens. Keep reading to learn about the thin lens equation and understand how a lens can magnify the image of an object. Everything is about light, so be sure to check out the principles of light refraction too!

Linear polarization diagram

The power (P) of a lens is the reciprocal of its focal length (f). Hence we can express the formula for the power of a lens as:

Let us consider five different situations for a converging lens (f > 0). You can check it with our thin lens equation calculator!

Linear polarization equation

Linearly polarized light is a special case of elliptically polarized light.  If the light is linearly polarized, then the two components oscillate in phase,  for example Ex = E0xexp(i(kz - ωt)), Ey = E0yexp(i(kz - ωt)), φ = 0.  The direction of E and the direction of propagation define a plane.  The electric vector traces out a straight line.  For example, E = Ei = E0xexp(i(kz - ωt))i.

We encourage you to check similar cases for the diverging lens, which has a negative focal length f < 0 with our calculator!

A quarter-wave plate δ = π/2 can be used to convert linearly polarized light to circularly polarized light.  The incident linearly polarized light must be oriented at 45o to the wave plate's axes.  A half-wave plate δ = π can be used to rotate the plane of linearly polarized light.  The angle of rotation is 2θ, where θ is the angle between the angle of polarization and the wave plate's fast axis.

Linear polarization definition

The electric field vector E can always be resolved into two perpendicular components.  The light is elliptically polarized, then the two components have a constant phase difference, and the tip of the electric field vector traces out an ellipse in the plane perpendicular to the direction of propagation.

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No, the thin lens formula is not different for different lenses. The thin lens formula is the same for both convex and concave lenses.

The two beams within the birefringent crystal are referred to as the ordinary and extraordinary ray, respectively.  The polarization of the extraordinary ray lies in the plane containing the direction of propagation and the optic axis, and the polarization of the ordinary ray is perpendicular to this plane.

The extraordinary ray violates both Snell’s Law and the Law of Reflection.  It is not necessarily confined to the plane of incidence.  Its speed changes with direction.  The index of refraction for the extraordinary ray is a continuous function of direction.  The index of refraction for the ordinary ray is independent of direction.  When the ordinary index of refraction is plotted against wavelength, the dispersion curve for the ordinary ray is a single unique curve.  The dispersion curve for the extraordinary ray is a family of curves with different curves for different directions.  A ray normally incident on a birefringent crystalline surface will be divided into two rays at the boundary, unless it is in a special polarization state or unless the crystalline surface is perpendicular to an optic axis.  The extraordinary ray will deviate from the incident direction while the ordinary ray will not.  The ordinary ray index n0 and the most extreme extraordinary ray index ne are together known as the principal indices of refraction of the material.  The direction of the lesser index is called the fast axis because light polarized in that direction has the higher speed.

You can compute the magnification of the created image, too (see the mirror equation calculator). It can be easily estimated if we know the distance of object x and the distance of image y: