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Questions
Draw a ray diagram of a refracting astronomical telescope when final image is formed at infinity. Also write the expression for its angular magnification (magnifying power).
Draw a labelled ray diagram of an astronomical telescope when the final image is formed at infinity. Write the expression for its magnifying power.
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Solution
In an astronomical telescope, the objective lens forms an intermediate real image, and the eye lens magnifies it.
- The object (e.g., a distant star) is placed far away, so the incoming rays are parallel.
- These parallel rays first pass through the objective lens, which converges them to form a real, inverted image at its focal point (Fo).
- The eye lens is then positioned such that this intermediate image lies at its focal point. As the eye lens diverges the rays, they appear to originate from infinity, creating the final image that is seen by the observer.
Magnifying power (Angular Magnification):
1. When the image is formed at a finite distance (e.g., at distance D):
The magnifying power is given by the formula:
M = `- f_o/f_e (1 + f_e/D)`
This formula takes into account the image formed at a distance D (closer than infinity).
2. When the image is formed at infinity (which is typical for astronomical telescopes):
The magnifying power simplifies to:
M = `- f_o/f_e`
This is the standard expression for magnifying power when the final image is at infinity.
RELATED QUESTIONS
Draw a schematic ray diagram of a reflecting telescope showing how rays coming from a distant object are received at the eyepiece.
- A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece of focal length 1.0 cm is used, what is the angular magnification of the telescope?
- If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.48 × 106 m, and the radius of lunar orbit is 3.8 × 108 m.
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- What is the height of the final image of the tower if it is formed at 25 cm?
Why should the objective of a telescope have large focal length and large aperture? Justify your answer.
Write two important advantages of reflecting telescope over a refracting telescope.
You are given three lenses of power 0.5 D, 4 D, and 10 D to design a telescope.
1) Which lenses should be used as objective and eyepiece? Justify your answer.
2) Why is the aperture of the objective preferred to be large?
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The eyepiece of an astronomical telescope has a focal length of 10 cm. The telescope is focussed for normal vision of distant objects when the tube length is 1.0. m. Find the focal length of the objective and the magnifying power of the telescope.
Draw a labelled ray diagram of an astronomical telescope in the near point adjustment position. A giant refracting telescope at an observatory has an objective lens of focal length 15 m and an eyepiece of focal length 1.0 cm. If this telescope is used to view the Moon, find the diameter of the image of the Moon formed by the objective lens. The diameter of the Moon is `3.48 xx 10^6`m, and the radius of the lunar orbit is `3.48 xx 10^8`m.
Draw a ray diagram of astronomical telescope for the final image formed at infinity.
