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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
A small telescope has an objective lens of focal length 144 cm and an eyepiece of focal length 6.0 cm. What is the magnifying power of the telescope? What is the separation between the objective and the eyepiece?
Draw a labelled ray diagram of an image formed by a refracting telescope with the final image formed at infinity. Derive an expression for its magnifying power with the final image at infinity
The focal lengths of the objective and eyepiece of a microscope are 1.25 cm and 5 cm respectively. Find the position of the object relative to the objective in order to obtain an angular magnification of 30 in normal adjustment.
A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece lens of focal length 1.0 cm is used, find 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 3.42 × 106 m and the radius of the lunar orbit is 3.8 × 108 m.
An astronomical telescope uses two lenses of powers 10 dioptres and 1 dioptre. If the final image of a distant object is formed at infinity, calculate the length of the telescope
Draw a labelled ray diagram showing the formation of an image by a refracting telescope when the final image lies at infinity.
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.
Draw a ray diagram of Astronomical Telescope for the final image formed at infinity
The magnifying power of an astronomical telescope in normal adjustment is 2.9 and the objective and the eyepiece are separated by a distance of 150 cm. Find the focal lengths of the two lenses.
Read the passage given below and answer the question that follows.
| There are two types of optical instruments: Microscopes and Telescopes. Microscopes are used to magnify very tiny objects whereas telescopes are used to study distant objects. Both of them deploy convex lenses. In his telescope, Newton used a large parabolic mirror to collect light from the stars and reduce aberrations. |
- Rohit observed the launch of Chandrayan 3 with the help of an optical instrument. Name the instrument used by him.
- State any one advantage of a reflecting telescope over a refracting telescope.
- Which instrument is used to study the structure of a virus?
- What is the ability of an optical instrument to form enlarged images called?
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What is the difference between a compound microscope and an astronomical telescope (refracting type), as far as their lenses are concerned?
Useful Constants & Relations:
| 1 | Charge of a proton | e | 1.6 × 10-19 C |
| 2 | Speed of light in vacuum | c | 3 × 108 ms-1 |
| 1 u = 931 MeV | |||
