A system of two lenses is achromatic when the separation between them is

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Joseph Hill
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1 L e c t u r e Eyepieces Single eye lens in a telescope / microscope produces spherical and chromatic aberrations. The field of view is also narrow. The eye lens is replaced by a system of lenses known as eyepiece. Modern day instruments use CMOS sensors instead of eyepieces and the images are observed on a computer screen. A system of two lenses is achromatic when the separation between them is A system of lenses reduces spherical aberrations if Huygen s Eyepiece It consists of two plano-convex lenses. The distance apart of the lenses should be half the sum of the focal lengths of the component lenses. It works well with long focal length telescopes. It is cheap to make, found in amateur or inexpensive optical instruments. And for no spherical aberrations 2 (field lens) 1 (objective lens) 1 image formed by the objective 2 image formed by of 1 image of 2 will be formed at infinity due to Observer sees the image at infinity with un-accommodated eye. The micrometer will be placed at 2. Its reading won t be reliable because image of the virtual object is formed by both the lenses while that of the scale by only one lens. Thus and

2 L e c t u r e Also known as negative eye-piece as the image formed by the objective lens is on the negative side of the field lens. Accurate measurements would not be possible as the cross wires on the scale would be viewed through the eye lens only, while the image would be seen by rays that have passed through both the lenses of the eyepiece. Huygens eyepieces consist of two plano-convex lenses with the plane sides towards the eye separated by an air gap. The lenses are called the eye lens and the field lens. Eye relief is 3 mm. Equivalent focal length Ramsden eyepiece 2 1 Consists of two plano convex lenses of equal focal length separated by a distance two-thirds of their common focal length and placed beyond the image formed by the objective.

3 L e c t u r e The real image from the objective is 1 is in front of the field lens. This is the position at which the crosswire must be placed and at which image due to objective is formed. Also known as positive eyepiece. It magnifies both the image and the cross wire equally. Eye relief is 12mm. Equivalent focal length Huygen s eyepiece 1. The image formed by the objective is behind the field lens. 2. Cross wires cannot be used. 3. Used where the object is illuminated by white light and measurements are not required. 4. The final image is convex towards the eye. Ramsden s eyepiece 1. The image formed by the objective is in front of the field lens. 2. Accurate measurement of the image can be carried out with the help of crosswires. 3. Used when only one wavelength region is viewed at a time and measurement are made. 4. The final image s almost flat. Spatial and Temporal coherence Principle of laser, stimulated and spontaneous emission. For an absorbing medium the intensity gets attenuated with distance. The attenuation is a function of frequency of the incoming wave

4 L e c t u r e I The number of atoms per unit volume that occupy a given energy level is called the population of that energy level. E 2 N 2 E 1 N 1 Let the populations at level E 1 be N 1 and at E 2 be N 2. At thermal equilibrium the population at the energy levels can be found from Boltzmann law The relative population is given by When a photon travels through a medium three different processes are likely to occur. They are absorption, spontaneous emission and stimulated emission. Absorption

5 L e c t u r e Rate of absorption transition can also be written as Where is population of atoms at, is the energy density of the incident beam and is the constant of proportionality also known as Einstein coefficient. Spontaneous Emission An atom cannot stay in an excited state for a longer duration. In a time of about 10-8 s, the atom reverts to the lower energy state by releasing a photon. Emission of a photon by an atom without any external impetus is called spontaneous emission. Stimulated Emission Electrons may make a downward transition with the interaction with photons. In stimulated emission each incident photon encounters a previously excited atom, and the optical field of the photon interacts with the electron. The result of the interaction is a kind of resonance effect, which induces each atom to emit a second photon with the same frequency, direction, phase and polarization as the incident photon. Einstein relations Under thermal equilibrium the mean population in the lower and upper energy levels should remain constant. As To maintain thermal equilibrium the system must release energy in the form of electromagnetic radiation. It is required that the radiation be identical with black body radiation and be consistent with Planck s radiation for any value of T.

6 L e c t u r e According to Planck s law Where the refractive index of the medium and c is is the velocity of light in free space. Thus and. The above relations are known as Einstein relations and the coefficients are known as Einstein coefficients. The relation also shows that the ratio of coefficients of spontaneous verses stimulated emissions proportion the third power of frequency of the radiation. This is why it is difficult to achieve laser action in higher frequency ranges such as x-rays.

A small object is placed a distance 2.0 cm from a thin convex lens. The focal length of the lens is 5.0 cm.

TC [66 marks] This question is about a converging (convex) lens. A small object is placed a distance 2.0 cm from a thin convex lens. The focal length of the lens is 5.0 cm. (i) Deduce the magnification