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An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 10 cm. An observer adjusts the distance of the eyepiece from objective to obtain the image of the sun on a screen 40 cm behind the eyepiece. The diameter of the sun's image is 6 cm. Find the diameter of the sun. The average earth sun distance is 1.5*10^11 m.?
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An astronomical telescope has an objective of focal length 200 cm and ...
Given:
- Focal length of the objective lens, f1 = 200 cm
- Focal length of the eyepiece, f2 = 10 cm
- Distance of the screen from the eyepiece, d = 40 cm
- Diameter of the sun's image on the screen, Dimage = 6 cm
- Average Earth-Sun distance, DES = 1.5 × 10^11 m
To Find:
- Diameter of the sun, Dsun
Formula:
The angular magnification of a telescope is given by:
M = -f1/f2
The angular magnification can also be expressed as the ratio of the apparent angular diameter of the image to the actual angular diameter of the object:
M = θimage/θsun
The actual angular diameter of the sun, θsun = Dsun/DES
The apparent angular diameter of the sun, θimage = Dimage/d
Calculation:
- Given that the distance between the objective and the eyepiece is adjusted to obtain the image on the screen, it implies that the final image is formed at the least distance of distinct vision (25 cm).
Using the formula for the angular magnification of the telescope, we have:
M = -f1/f2
=> M = -200 cm/10 cm
=> M = -20
Using the formula for the ratio of the apparent angular diameter to the actual angular diameter, we have:
M = θimage/θsun
=> -20 = (6 cm/40 cm) / θsun
=> -20 = 0.15 / θsun
=> θsun = -0.15/20
=> θsun = -0.0075 radians
The negative sign indicates that the image formed is inverted.
Using the formula for the actual angular diameter of the sun, we have:
θsun = Dsun/DES
=> -0.0075 radians = Dsun / (1.5 × 10^11 m)
=> Dsun = -0.0075 radians × (1.5 × 10^11 m)
=> Dsun = -1.125 × 10^9 radians × m
Answer:
The diameter of the sun is approximately 1.125 × 10^9 radians × meters.
- Focal length of the objective lens, f1 = 200 cm
- Focal length of the eyepiece, f2 = 10 cm
- Distance of the screen from the eyepiece, d = 40 cm
- Diameter of the sun's image on the screen, Dimage = 6 cm
- Average Earth-Sun distance, DES = 1.5 × 10^11 m
To Find:
- Diameter of the sun, Dsun
Formula:
The angular magnification of a telescope is given by:
M = -f1/f2
The angular magnification can also be expressed as the ratio of the apparent angular diameter of the image to the actual angular diameter of the object:
M = θimage/θsun
The actual angular diameter of the sun, θsun = Dsun/DES
The apparent angular diameter of the sun, θimage = Dimage/d
Calculation:
- Given that the distance between the objective and the eyepiece is adjusted to obtain the image on the screen, it implies that the final image is formed at the least distance of distinct vision (25 cm).
Using the formula for the angular magnification of the telescope, we have:
M = -f1/f2
=> M = -200 cm/10 cm
=> M = -20
Using the formula for the ratio of the apparent angular diameter to the actual angular diameter, we have:
M = θimage/θsun
=> -20 = (6 cm/40 cm) / θsun
=> -20 = 0.15 / θsun
=> θsun = -0.15/20
=> θsun = -0.0075 radians
The negative sign indicates that the image formed is inverted.
Using the formula for the actual angular diameter of the sun, we have:
θsun = Dsun/DES
=> -0.0075 radians = Dsun / (1.5 × 10^11 m)
=> Dsun = -0.0075 radians × (1.5 × 10^11 m)
=> Dsun = -1.125 × 10^9 radians × m
Answer:
The diameter of the sun is approximately 1.125 × 10^9 radians × meters.
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An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 10 cm. An observer adjusts the distance of the eyepiece from objective to obtain the image of the sun on a screen 40 cm behind the eyepiece. The diameter of the sun's image is 6 cm. Find the diameter of the sun. The average earth sun distance is 1.5*10^11 m.?
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An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 10 cm. An observer adjusts the distance of the eyepiece from objective to obtain the image of the sun on a screen 40 cm behind the eyepiece. The diameter of the sun's image is 6 cm. Find the diameter of the sun. The average earth sun distance is 1.5*10^11 m.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 10 cm. An observer adjusts the distance of the eyepiece from objective to obtain the image of the sun on a screen 40 cm behind the eyepiece. The diameter of the sun's image is 6 cm. Find the diameter of the sun. The average earth sun distance is 1.5*10^11 m.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 10 cm. An observer adjusts the distance of the eyepiece from objective to obtain the image of the sun on a screen 40 cm behind the eyepiece. The diameter of the sun's image is 6 cm. Find the diameter of the sun. The average earth sun distance is 1.5*10^11 m.?.
An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 10 cm. An observer adjusts the distance of the eyepiece from objective to obtain the image of the sun on a screen 40 cm behind the eyepiece. The diameter of the sun's image is 6 cm. Find the diameter of the sun. The average earth sun distance is 1.5*10^11 m.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 10 cm. An observer adjusts the distance of the eyepiece from objective to obtain the image of the sun on a screen 40 cm behind the eyepiece. The diameter of the sun's image is 6 cm. Find the diameter of the sun. The average earth sun distance is 1.5*10^11 m.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 10 cm. An observer adjusts the distance of the eyepiece from objective to obtain the image of the sun on a screen 40 cm behind the eyepiece. The diameter of the sun's image is 6 cm. Find the diameter of the sun. The average earth sun distance is 1.5*10^11 m.?.
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An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 10 cm. An observer adjusts the distance of the eyepiece from objective to obtain the image of the sun on a screen 40 cm behind the eyepiece. The diameter of the sun's image is 6 cm. Find the diameter of the sun. The average earth sun distance is 1.5*10^11 m.?, a detailed solution for An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 10 cm. An observer adjusts the distance of the eyepiece from objective to obtain the image of the sun on a screen 40 cm behind the eyepiece. The diameter of the sun's image is 6 cm. Find the diameter of the sun. The average earth sun distance is 1.5*10^11 m.? has been provided alongside types of An astronomical telescope has an objective of focal length 200 cm and an eyepiece of focal length 10 cm. An observer adjusts the distance of the eyepiece from objective to obtain the image of the sun on a screen 40 cm behind the eyepiece. The diameter of the sun's image is 6 cm. Find the diameter of the sun. The average earth sun distance is 1.5*10^11 m.? theory, EduRev gives you an
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