Astronomical Telescope

The main reason for a distant object to be smaller is that the two objects subtend different angles at the eye. In other words, we can say that different angles subtended by the eye causes a distant object to appear smaller.

The object AB and CD are of the same height. The object CD is closer to the eye than AB.

The object CD appears to be taller than AB because angle B that CD subtends at the eye is greater than the angle x subtended by AB at the eye. Images there can be made to appear large by bringing them closer to the eye.

In a telescope, the final image is magnified because it subtends a much greater angle at the eye than does a distant object observed without a telescope. B is the angle subtended by the final image at the eye and X is the angle subtended by a distant object.

The magnification of a telescope is defined as the ratio of the angel B (in radians) subtended by the final image at the eye to the angle X subtended by a distant object at the eye.

Thus, for telescope the magnification is given by:

$M = B/x$ ………………………………….i

From figure $B = IQ/ID$ ……………………. .ii

$X = IQ/IA$ ……………………………………….. iii

But Insert eqn (ii) and (iii) into eqn (i)

$M = (12/ID)$

$(IQ/IA)$

$M = (IA/ID)$

But $IA = f_o$ and $IF = f_e$

$M = f_o/f_e$ ……………………………….(x)

$f_o$ is the focal length of two thin converging lenses of focal lengths 25cm and 4cm respectively. It is focused on the moon, which subtends an angle of 0.6° at the objective lens. The final image is formed at the observers least distance of distinct vision (25cm in front of the eyepiece). Find the diameter of this image. In the previous figure:

$X = h/f_o$

Where $f_o$ is the focal length of the objective lens

$X = h/25$

Where X is the angle in radians subtended at the objective lens by the moon.

$H = 25x$

$H = 25 (6/10 \times 11/180)$

$H = 25 (6/10 \times 22/7 \times 1/80)$

$H = 0.2619m$

The height of the image, h = 0.2619m

The distance of this image from the eyepiece is obtained from the relation:

1. $I/U + I/V = I/f_e = 4cm$
2. $V = -25cm$
3. $I/U - I/25 = 1/4$
4. $I/U = (1/4 + 1/25)$
5. $(I/U)^{-1} = (25 + 4)^{-1}/100$
6. $100U = (100/29)$
7. The magnification, m of the lens:
8. $M = V/u$
9. $M = (25CM/100/29)$
10. $M = 29/4$
11. Let the height of the final image of the moon be h:
12. $M = H_i/h$
13. $h_I = mh$
14. $H_I = (29/4)(0.2619)$
15. $H_I = 1.90cm$

The Height of image $H_i$ = 1.9cm

1. Telescopes see many colors - telescopes can collect light that our eyes are unable to: radio, microwave, infrared, ultraviolet, x-rays and gamma rays.
2. Telescopes collect lots of light - our pupils are only a few millimeters across, so we can only collect photons over a tiny area whereas telescopes can collect photons of huge areas (e.g. a football fields worth for radio telescopes).
3. Telescopes see fine details because of the wave nature of light and the nerves in our eyes, we can only see details about the same angular size as Jupiter's width. Telescopes can allow us to resolve fine details - like Jupiter's Great Red Spot.
4. Telescopes can record observations with cameras - You can see things with your eye and draw them, but telescopes can share observations with the world! This is especially important for convincing skeptics that what you saw was real