Visual Angle How large an object appears, and how much detail we can see on it, depends on the size of the image it makes on the retina. This, in turns, depends on the angle subtended by the object at the eye. 11 22

Magnifying Glass (Simple Microscope) A magnifying glass allows us to place the object closer to our eye so that it subtends a greater angle. The object is placed within the focus of the lens so as to produce a virtual image, which must be at least 25 cm (least distance of distinct vision or near point) from the eye.

Magnifying Power of a simple microscope (Angular Magnification) Where  is the angle subtended by the object at the near point of the eye and  is the angle subtended by the image to the lens. M is the ratio of the apparent sizes of the image and the object. 

Compound microscope A microscope is used to produce an image on the retina larger than that obtainable by placing a small accessible object at the near point. The overall magnification of a microscope is the product of the magnifications produced by the two lenses.

Compound Microscope in Normal Adjustment In normal adjustment an enlarged virtual image is formed at the near point, 25 cm from the normal eye. D (25 cm)  Objective Eyepiece

Magnifying Power of a compound Microscope In normal adjustment, the angular magnification equals the linear magnification Where  is the angle subtended by the object at the near point of the eye and  is the angle subtended by the final image at the eye.

Resolution of Lens The ability of a lens to produce distinct images of two point objects very close together is called the resolution of the lens. The closer the two images can be and still be seen as distinct, the higher the resolution. Image of pollen grain with good resolution (left) and poor resolution (right)

Resolving Power of a Microscope The resolving power of a microscope is its ability to enable detail in the image to be made out. The resolving power depends on The aperture of the objective (The larger the aperture, the better the resolution.) The wavelength of the light (The shorter the wavelength, the better the resolution.)

The Eye Ring for a Microscope The eye ring is the optimum position for the observer’s eye to gather most light that passing through the objective. The image is then brightest and the field of view greatest. The eye ring is also the image of the objective formed by the eyepiece. An observer should ideally have a pupil diameter equal to the eye ring.

Modern Microscope Component Configuration

Refracting Telescope A telescope is used to produce an enlarged retinal image of a distant inaccessible object. The job of a telescope Light gathering power Magnifying power Resolving power

Magnifying Power of a Refracting Telescope Where  is the angle subtended at the eye by the object without the telescope,  is the angle subtended by the final image at the eye.

Refracting Telescope in Normal Adjustment In normal adjustment the final image seen through the eyepiece is adjusted to line at infinity so that the eye is the most relaxed. In normal adjustment, The length of a telescope in normal adjustment = f o +f e

Resolving Power of a Telescope (1) Resolving power of a telescope is the ability to separate two closely positioned stars. Diffraction by the objective is a factor that limits the resolving power of a telescope.

Resolving Power of a Telescope (2) The resolving power of a telescope depends on the quality of the optical surfaces, depends on the wavelength observed, increases as the diameter of the objective increases. Large lenses are difficult to make and they tend to sag under their own weight.

The Eye Ring for a Telescope In normal adjustment, it can be shown that

Reflecting Astronomical Telescope Advantages of reflecting telescope: No chromatic aberration A mirror can have a much larger diameter than a lens No spherical aberration if paraboloidal mirror is used

Hubble Space Telescope Eskimo nebula HST’s primary mirror Eagle nebula

Terrestrial Telescope This system has the disadvantage of increasing the length of the telescope. An advantage is that it makes it possible to vary the magnification of the telescope. An erecting lens is inserted between the objective and the eye piece to erect the inverted image formed by the objective.

Galilean Telescope Advantages: The final image is erect so it is useful for terrestrial purposes. It is shorter than the terrestrial telescope Disadvantages: Small field of view

Spectrometer The spectrometer is an instrument used for Producing, viewing and taking measurements on a pure spectrum using either a prism or a diffraction grating. Measuring accurately the refractive index of a material in the form of a prism.

Construction of a spectrometer The essential parts are The collimator which is fixed to the base of the instrument, consisting of a slit of variable width, and an achromatic lens. The turntable, which can be rotated, and to which a prism or grating can be attached. The circular edge of the table has a scale graduated in degrees. The telescope, which can also be rotated. A vernier scale is fitted to the telescope where it adjoins the table, enabling their relative orientation to be measured to 0.1 o, or less.

Functions of the collimator and the telescope (1) Spectrometer used to measure wavelength of light Light source Collimator C Achromatic lenses Diffraction grating Telescope T Eyepiece Eye θ Cross-wire Turntable

Functions of the collimator and the telescope (2) The collimator is set to produce a parallel beam of light from the light source near the slit. The telescope is set to receive parallel beam of light and hence measures the angle of deviation of light through the diffraction grating or the prism.

Adjustments of the spectrometer The eyepiece is focussed on the crosswires. The objective lens of the telescope is focussed so that the crosswires are in its focal plane. Using a slit of width appropriate to the source brightness, the collimator lens is moved so that the slit is in its focal plane. Using the table levelling screws, the axis of the table is made perpendicular to the plane containing the principal axes of the collimator and telescope lenses.