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प्रश्न
Draw a ray diagram for the formation of image of an object by an astronomical telescope, in normal adjustment. Obtain the expression for its magnifying power.
उत्तर
The illustration displays an astronomy telescope used to provide angular magnification of distant objects. It sports a big diameter objective lens with a long focal length. The diameter and focal length of the eyepiece are both smaller than those of the objective lens. When light from a distant object enters the objective, an actual image is formed in the tube at its second focal point. The eyepiece enlarges this image, resulting in the final inverted image. The "tube length" or distance between the objective and the eyepiece, is the sum of the focal lengths of the two lenses when their innermost points meet.
The angle “β” that the picture subtends at the eye compared to the angle “α” that the object subends at the lens is the magnifying power or m.
`m = (beta/alpha)`
`beta = tanbeta = h/f_e`
Where h is image height and fe is focal length of eyepiece.
`alpha = tanalpha = h/f_o`
Where fo is focal length of objective lens.
Hence, we get magnifying power m as,
`m = (h"/"f_e)/(h"/"f_o) = f_o/f_e`
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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?
Define magnifying power of a telescope. Write its expression.
An astronomical telescope is to be designed to have a magnifying power of 50 in normal adjustment. If the length of the tube is 102 cm, find the powers of the objective and the eyepiece.
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
Define the term 'resolving power of a telescope'. How will the resolving power be effected with the increase in
(i) Wavelength of light used.
(ii) Diameter of the objective lens.
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 showing the image formation by a refracting telescope. Define its magnifying power.
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.
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.
