Draw a labelled ray diagram of an astronomical telescope in the near point adjustment position. A giant refracting telescope at an observatory has an objective lens of focal length 15 m and an eyepiece of focal length 1.0 cm. If this telescope is used to view the Moon, find the diameter of the image of the Moon formed by the objective lens. The diameter of the Moon is 3.48 × 10 6 m, and the radius of lunar orbit is 3.8 × 10 8 m.

Question

Philoid · Accepted Answer

Concepts/Formulas used:

The lens equation:

The lens formula is:
where f is the focal length, u is the object distance and v is the image distance. All quantities are measured with the cartesian sign convention (the sign convention in NCERT).

We have,

To find the image position, we can take the

Object distance,
Focal length,

Using the lens equation,

(As the object distance is very much larger than the focal length, we can take it as infinity)

Now,

The objective lens forms the image of the moon.

Diameter of the moon/Height of the object .

Let the diameter of the image be

We know that,

The negative sign indicates that the image is inverted. Hence, the diameter of the image of the moon is 13.7 cm.