Terrestrial Telescope Adjustment

A terrestrial telescope is a type of telescope designed for observing objects on Earth rather than celestial objects. It is commonly used for activities such as birdwatching, nature observation, and surveillance. In normal adjustment, the telescope consists of an objective lens, an eyepiece, and an erecting lens.

Given Information:
- Objective lens focal length (f1) = 180 cm
- Eyepiece focal length (f2) = 6 cm
- Erecting lens focal length (f3) = 3.5 cm

Calculating the Length of the Telescope:

To calculate the length of the telescope in normal adjustment, we need to consider the lens formula and the magnification formula.

Lens Formula:
The lens formula relates the object distance (u), the image distance (v), and the focal length (f) of a lens. It is given by:

1/f = 1/v - 1/u

Magnification Formula:
The magnification (m) of a telescope is the ratio of the angular size of the image formed by the objective lens to the angular size of the object being observed. It is given by:

m = -v/u

Deriving the Formula for Length of the Telescope:

The length of the telescope can be calculated using the lens formula and magnification formula as follows:

1/f1 = 1/v1 - 1/u1 (For objective lens)
1/f2 = 1/v2 - 1/u2 (For eyepiece)
1/f3 = 1/v3 - 1/u3 (For erecting lens)

The magnification (m) is given by:
m = -v1/u1 = v2/u2 = -v3/u3

In normal adjustment, the image formed by the objective lens is at infinity (v1 = ∞). Therefore, the object distance for the eyepiece (u2) is equal to the focal length of the objective lens (f1).

u2 = f1 = 180 cm

Using the lens formula for the eyepiece, we can calculate the image distance (v2):

1/f2 = 1/v2 - 1/u2
1/6 = 1/v2 - 1/180
1/v2 = 1/6 + 1/180
1/v2 = 30/180
v2 = 6 cm

The object distance for the erecting lens (u3) is equal to the image distance of the eyepiece (v2).

u3 = v2 = 6 cm

Using the lens formula for the erecting lens, we can calculate the image distance (v3):

1/f3 = 1/v3 - 1/u3
1/3.5 = 1/v3 - 1/6
1/v3 = 1/3.5 + 1/6
1/v3 = 6/21 + 3.5/21
1/v3 = 9.5/21
v3 = 2.21 cm

The length of the telescope can be calculated by adding the distances between the lenses:

Length = u1 + u2 + u3
Length = f1 + f2 + f3
Length = 180

200cm