Lecture 8: Optical instruments
Lecture aims to explain:
1. Magnifying power
3. Microscope, principle of operation
4. Telescope, principle of operation Magnifying power Magnifying power
The magnifying power or angular magnification of a visual instrument is defined as:
the ratio of the size of the retinal image as seen through the instrument over the size of the retinal image as seen by the unaided eye at normal viewing distance (or the near point)
This is equivalent to the ratio of the angles (assisted over unaided) α MP = a α αu u do do distance to the near point (~25 cm) Magnifying glass Magnifying glass Use a positive lens to increase the size of the retinal image relative to that with the unaided eye: magnified virtual image is formed
f do l Magnification is given by Example 8.1 do 1 MP = 1+ (L − l) Find magnification of a magnifying L f glass, if the object is positioned at the focal point of the lens
L distance to the image, do distance to the near point (~25 cm) Microscope Compound microscope Two convex lenses, usually with fixed distance between them
1. Objective near the specimen, creates a real image in the focal plane of the eyepiece. Specimen placed near the focal point of the objective
2. Eyepiece near the eye, works as magnifying glass, creates virtual image for viewing with an unaccommodated eye
Magnification when the final image Objective Eyepiece is viewed at infinity: L d MP = − o fe fo fe fo L distance from the focal point of the objective to the image, do near point L (~25 cm) Telescope Refracting telescope
Two convex lenses with adjustable distance between them
1. Objective creates a real image in its focal plane as objects are very far away.
2. Eyepiece, works as magnifying glass, creates a virtual image for viewing with an unaccommodated eye
Objective Eyepiece Magnification is given by
f f f MP = − o o e fe
fo + fe Example 8.2: Galilean telescope
A Galilean telescope has an objective lens of 12cm focal length and an eyepiece of 5cm focal length. It is focused on a distant object so that the final image seen by the eye appears to be at a distance of 30cm from the eyepiece. Determine the angular magnification.
Figure shows an example of Galilean telescope when the image is viewed at infinity: objective is convex and eyepiece is concave Example 8.3: microscope
The eyepiece and objective of a microscope are 20.6cm apart, and each has a focal length of 0.6cm. Find a) the distance from objective to the object viewed b) the linear magnification produced by the objective c) the overall magnifying power. Assume throughout the final image is formed at infinity. SUMMARY The magnifying power: the ratio of the size of the retinal image as seen through the instrument over the size of the retinal image as seen by the unaided eye at normal viewing distance (or the near point)
Magnifying glass: a single positive lens. do Magnification for an unaccommodated eye: MP = fe Microscopes and telescopes can be assembled using two convex lenses. Microscope: objective creates a real magnified image in the focal plane of the eyepiece. Telescope: objective creates a real image in its focal plane, coinciding with the focal plane of the eyepiece.
For viewing with an unaccommodated eye the magnifying power for telescope: f microscope: L d MP = − o MP = − o fe fo fe