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प्रश्न
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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उत्तर
In an astronomical telescope, the objective lens forms an intermediate real image, and the eyepiece 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 eyepiece lens is then positioned such that this intermediate image lies at its focal point. As the eyepiece 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.
संबंधित प्रश्न
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?
With regard to an astronomical telescope of refracting type~ state how you will increase its:
1) magnifying power
2) resolving power
Describe briefly the two main limitations and explain how far these can be minimized in a reflecting telescope ?
Define its magnifying power and write the expression for it?
A Galilean telescope is 27 cm long when focussed to form an image at infinity. If the objective has a focal length of 30 cm, what is the focal length of the eyepiece?
(i) What is meant by resolving power of a telescope?
(ii) State any one method of increasing the resolving power of an astronomical 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.
A small telescope has an objective lens of focal length 140 cm and an eyepiece of focal length 5.0 cm. Find the magnifying power of the telescope for viewing distant objects when
- the telescope is in normal adjustment,
- the final image is formed at the least distance of distinct vision.
In an astronomical telescope in normal adjustment, a straight black line of length L is drawn on the objective lens. The eyepiece forms a real image of this line whose length is 𝑙. What is the angular magnification of the telescope?
Assertion: An astronomical telescope has an objective lens having large focal length.
Reason: Magnifying power of an astronomical telescope varies directly with focal length of the objective lens.
