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Complete Question
Due to blurring caused by atmospheric distortion, the best resolution that can be obtained by a normal, earth-based, visible-light telescope is about 0.3 arcsecond (there are 60 arcminutes in a degree and 60 arcseconds in an arcminute).Using Rayleigh's criterion, calculate the diameter of an earth-based telescope that gives this resolution with 700 nm light
Answer:
The diameter is
Explanation:
From the question we are told that
The best resolution is
The wavelength is
Generally the
1 arcminute = > 60 arcseconds
=> x arcminute => 0.3 arcsecond
So
=>
Now
60 arcminutes => 1 degree
0.005 arcminutes = > z degrees
=>
=>
Converting to radian
Generally the resolution is mathematically represented as
=>
=>
=>
Answer: f=150cm in water and f=60cm in air.
Explanation: Focal length is a measurement of how strong light is converged or diverged by a system. To find the variable, it can be used the formula:
= (nglass - ni)(
-
).
nglass is the index of refraction of the glass;
ni is the index of refraction of the medium you want, water in this case;
R1 is the curvature through which light enters the lens;
R2 is the curvature of the surface which it exits the lens;
Substituting and calculating for water (nwater = 1.3):
= (1.5 - 1.3)(
-
)
= 0.2(
)
f = = 150
For air (nair = 1):
= (1.5 - 1)(
-
)
f = = 60
In water, the focal length of the lens is f = 150cm.
In air, f = 60cm.