If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the image of the tower formed by the objective lens? - Physics

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Numerical

If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the image of the tower formed by the objective lens?

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Solution

Focal length of the objective lens, fo = 140 cm

Focal length of the eyepiece, fe = 5 cm

Height of the tower, h1 = 100 m

Distance of the tower (object) from the telescope, u = 3 km = 3000 m

The angle subtended by the tower at the telescope is given as:

θ = `"h"_1/"u"`

= `100/3000`

= `1/30` rad

The angle subtended by the image produced by the objective lens is given as:

θ = `"h"_2/"f"_"o" = "h"_2/140 "rad"`

Where,

h2 = Height of the image of the tower formed by the objective lens

`1/30 = "h"_2/140`

∴ `"h"_2 = 140/30` = 4.7 cm

Therefore, the objective lens forms a 4.7 cm tall image of the tower.

Concept: Optical Instruments: Telescope
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Chapter 9: Ray Optics and Optical Instruments - Exercise [Page 347]

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NCERT Physics Class 12
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 9.29 (b) | Page 347
NCERT Physics Class 12
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 35.2 | Page 349

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