Angular Magnification of a Giant Refracting Telescope
A giant refracting telescope has an objective lens of focal length 15 m and an eyepiece of focal length 1.0 cm. We calculate:
(b) Diameter of the image of the Moon formed by the objective
Part (a): Angular Magnification
For a telescope in normal adjustment:
fe = 1.0 cm = 0.01 m
Answer (a)
Part (b): Diameter of Image of the Moon
Angular size of Moon:
Image formed at focal plane:
Answer (b)
Thus, the telescope produces an angular magnification of 1500 times, and the objective forms a real image of the Moon about 14 cm in diameter.
Frequently Asked Questions
What is the formula for angular magnification of a refracting telescope?
For a telescope in normal adjustment, the angular magnification is given by M = fo / fe, where fo is the focal length of the objective and fe is the focal length of the eyepiece.
Why is the angular magnification so large for observatory telescopes?
Observatory telescopes use very large focal length objectives and very small focal length eyepieces. This makes the ratio fo / fe very large, resulting in high angular magnification.
How is the diameter of the Moon’s image calculated?
The objective forms a real image at its focal plane. The image diameter is given by Image size = fo × θ, where θ is the angular size of the Moon.
Why is the image formed by the objective real?
The objective lens focuses parallel rays coming from distant objects (like the Moon) at its focal plane, forming a real, inverted image.
What are the final results of this problem?
The angular magnification of the telescope is 1500, and the diameter of the Moon’s image formed by the objective is approximately 13.7 cm.
Theory: Refracting Telescope
1. Construction and Basic Principle
A refracting telescope consists of two convex lenses:
Refracting Telescope – Complete Theory
A refracting telescope is an optical instrument used to observe distant objects such as planets, stars, and the Moon. It works by collecting parallel rays of light using a large objective lens and magnifying the image using an eyepiece.
🔹 1. Construction of a Refracting Telescope
• Large focal length
• Large aperture
• Forms a real, inverted image
• Small focal length
• Acts as a magnifier
• Enlarges the image formed by the objective
🔹 2. Working Principle
Light from distant celestial objects arrives at the telescope as nearly parallel rays. The objective lens focuses these rays at its focal plane, forming a real image. The eyepiece then magnifies this image to increase angular size.
M = fo / fe
🔹 3. Image Formation by Objective
The size of the image formed at the focal plane depends on the angular size of the object.
Where θ is the angular size in radians.
🔹 4. Why Observatory Telescopes Have Huge Magnification
Large telescopes use extremely long focal length objectives and short focal length eyepieces. Since magnification depends on the ratio fo / fe, a large ratio produces very high angular magnification.
Smaller fe → Greater magnification
This is why giant refracting telescopes can produce detailed images of distant celestial bodies.
• Eyepiece – Small focal length
The objective lens collects light from distant objects (like the Moon) and forms a real, inverted image at its focal plane. The eyepiece then acts as a magnifier and enlarges this image for the observer.
2. Normal Adjustment of Telescope
In normal adjustment, the final image is formed at infinity. This allows comfortable viewing because the eye remains relaxed.
M = fo / fe
Where:
fe = Focal length of eyepiece
3. Image Formation by the Objective
For distant astronomical objects, light rays reaching the telescope are nearly parallel. The objective forms the image at its focal plane.
Where:
4. Why Large Telescopes Have High Magnification
Observatory telescopes use very large focal length objectives and small focal length eyepieces. Since magnification depends on the ratio fo / fe, increasing this ratio greatly increases angular magnification.
Smaller fe → Greater magnification
Thus, giant refracting telescopes produce highly magnified and detailed images of distant celestial bodies.