# 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

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?

#### 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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#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 9.29 (b) | Page 347
NCERT Class 12 Physics Textbook
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 35.2 | Page 349
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