(a)A giant refracting telescope at an observatory has an objective lens of focal length 15m. If an eyepiece of focal length 1.0cm is used, what is the angular magnification of the telescope?
(b)If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.48×106m, and the radius of the lunar orbit is 3.8×108m.
(a)A giant refracting telescope at an observatory has an objective lens of focal length 15m. If an eyepiece of focal length 1.0cm is used, what is the angular magnification of the telescope?
(b)If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.48×106m, and the radius of the lunar orbit is 3.8×108m.
Solution and Explanation
The focal length of the objective lens,fo=15m=15×102cm
Focal length of the eyepiece,fe=1.0cm
(a)The magnification of a telescope is given as \(\alpha = \)\(\frac{f_o}{f_e}\)=15×102=1500
Hence, the angular magnification of the given refracting telescope is 1500.
(b)Diameter of the moon,d=3.48×106m
The radius of the lunar orbit,r0=3.8×108m
Let d' be the diameter of the image of the moon formed by the objective lens. The angle subtended by the diameter of the moon is equal to the angle subtended by the image.
\(\frac{d}{r_o}\)=\(\frac{d'}{f_o}\)=\(\frac{3.48\times 10^6}{3.8\times 10^8}\)=\(\frac{d'}{15}\)
∴ d'=\(\frac{3.48}{3.8}\)×10-2×15=13.74×10-2m=13.74cm
Hence, the diameter of the moon's image formed by the objective lens is 13.74cm.
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Concepts Used:
Ray Optics and Optical Instruments
Optics, deals with the determination of behaviour and the properties of light, along with its interactions with the matter and also with the instruments that are used to detect it.
Ray optics is also known as the geometrical optics and it is a branch of science which describes light propagation.
Reflection is the change in direction of light at an interface in-between two different media so that the wave-front returns into a medium from which it was originated.
Speed of light is the rate at which the light travels in free space.
A phenomenal change in image formed when the light is passed from one medium to another which is called Refraction.
Total Internal Reflection is the reflection of light when the light ray enters into a rarer medium from a denser medium and the angle of incidence is higher than the critical angle of incidence then that light ray will be reflected back to the denser medium.
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