^Polarisation

A wave having vibrations is only in one direction & that is normal to its direction of propagation is called a polarized wave & the phenomenon of restricting the oscillation of a wave to just one direction in a direction transverse plane or normal to its direction of propagation is called polarisation of waves. Only transverse waves can be polarized or longitudinal waves can’t be polarized. Any transverse wave can be linearly polarized in any direction perpendicular to the direction of propagation.

^Resolving power of a compound microscope

Here, λ = wavelength of light used

μ = refractive index of the medium between the object & objective lens

θ = Half angle of the cone of light from each point object.

Also μ sinθ is called numerical aperture.

From above relation it is clear that the resolving power of a compound microscope can be increased by increasing refractive index of the medium. It is due to this reason that oil immersion objectives are used to increase the resolving power. Also, higher the value of numerical aperture, larger will be the resolving power of the microscope.

^Resolving limit of human eye

For human eye resolving limit is one  minute (abbreviated as, 1), this means that the human eye can see two point objects separately if they subtend angle more than one minute of arc at the eye. The diameter of the pupil of human eye is about 2 mm. If we use λ= 5000 A⁰ to see objects, then the smallest angular separation between two distant point objects that the human eye can resolve is

Thus the human eye can see two point objects distinctly if they at the eye an angle equal to one minute of arc. This angle is called the limit of resolution of the eye.

Light rays coming from any object after passing through pupil & eye lens get focused on the retina (screen) in the form of diffraction pattern. We know the maximum intensity of light is diffracted mainly in the central maxima. If the light rays is coming from two objects situated either too close to each other or very far away from eye then their central maxima of their diffraction pattern overlap at the retina, stimulating almost same cells on retina & brain gets one signal & we have perception that we are viewing one object in other words eye fails to resolve (or separate) the two objects if they subtend small angles at eye. e.g. a vehicle with its head lamps ON is approaching us. When the distance of the vehicle from us is large then the angle subtended by the head lamps at the eye is very small, if this is less than one minute then the diffraction pattern of their images at the retina overlap & we have perception of one head lamp. But as the vehicle approaches us the angle subtended by the head lamps at the eye increases, once this angle is more than one minute of arc, diffraction pattern of their images at the retina are formed at different points, exciting retina cells at two different & there by sending two signals to brain & we have perception of two different head lamps now.

Due to the same reason we fail to resolve two nearby stars.

^Resolving limit

Inability of an optical instrument (eye, microscope, telescope) to resolve the separation of two objects is called its resolving limit or limit of resolution & can be define as the smallest linear or angular separation between two points that can be just resolved i.e. visible distinctly & clearly by it.

^Resnel’s distance (DF)

The distance of the screen from the slit at which the diffraction spread of a beam is equal to the size of the aperture of the slit is called Fresnel’s distance. i.e., when y = d, D = D_F, thus  

For a given value of d the quantity  is called the size of Fresnel zone and is denoted by d_F.

Geometrical optics or ray optics is based upon the rectilinear propagation of light. If D < D_F, then there will not be too much broadening by diffraction i.e., the light will travel along straight lines and the concepts of ray optics will be valid.