Optical Instruments — Part 2: Telescopes and resolving power: visual lesson, ISC Class 12 Physics

Lesson

Telescopes and Resolving Power

Part 2 — bringing distant objects closer, and the limit to how much detail any instrument can show.

In this lesson you will

Derive the magnifying power of a refracting astronomical telescope in normal adjustment and with the image at D
Draw a Cassegrain reflecting telescope and give its advantages over a refractor
State the factors that fix the resolving power of a microscope, and list uses, advantages and drawbacks of optical instruments

Concept

The refracting astronomical telescope

Two converging lenses on a common axis:

Objective: long focal length $f_o$ and large aperture, to collect plenty of light from the distant object and form a real image at its focus.
Eyepiece: short focal length $f_e$ , a magnifier for that image.
The object cannot be brought closer, so α is the angle it subtends where it is (practically, at the objective or the eye).

Table comparing the objective and the eyepiece of a refracting telescope: focal length, aperture and job
Lens	Focal length	Aperture	Job
Objective	Long (e.g. 80 cm–2 m)	Large	Collects light, forms a real image at F_o
Eyepiece	Short (a few cm)	Small	Magnifies that image

Diagram

Normal adjustment: image at infinity

Rays from the top of a distant object arrive parallel at angle α. The objective focuses them to I in its focal plane, a height $h$ below the axis: $\alpha = \dfrac{h}{f_o}$ . In normal adjustment I is also at the focus of the eyepiece, so the rays leave parallel at angle $\beta = \dfrac{h}{f_e}$ : $M = \dfrac{\beta}{\alpha} = \dfrac{f_o}{f_e},\qquad L = f_o + f_e$

The final image is at infinity and inverted.

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