Resolving Distant Objects question

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In summary, the question is about resolving distant objects using a telescope with a small circular aperture. The relevant equation is sin(theta) = 1.22 x lambda/D, and the maximum wavelength at which two point sources can be resolved is calculated to be 0.492 nm. However, it is clarified that the correct wavelength is 492 nm, not 0.492 nm.
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fatkat444
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[SOLVED] Resolving Distant Objects question

Consider a telescope with a small circular aperture of diameter 2.0 centimeters.

If two point sources of light are being imaged by this telescope, what is the maximum wavelength (lambda) at which the two can be resolved if their angular separation is 3.0 x 10^-5 radians?



Relevant equation - sin(theta) = 1.22 x lambda/D


I get - Dsin(theta)/1.22 = lambda
0.02 x sin(3.0 x 10^-5)/1.22 = lambda
= 4.92 x 10^-7
therefore lambda = 0.492 nm

It doesn't seem correct. Any help would be very appreciated.
 
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  • #2
You're correct its just you have the units confused. It will be 492nm not 0.492. Remember a nanometer is 1 billionth of a meter. So one nanometer is 1x10-9 m.
 
  • #3
yeah i just figured it out and was coming back to post as you replied, thanks anyway though.
 

1. How do we determine the distance of an object in space?

The distance of an object in space can be determined through various methods such as parallax, redshift, and standard candles. Parallax involves measuring the apparent shift in the position of an object when viewed from different angles. Redshift is a phenomenon where an object's light appears to shift towards the red end of the spectrum due to its motion away from us. Standard candles are objects with known luminosity, such as certain types of stars, which can be used to estimate distance based on their apparent brightness.

2. Why is it difficult to measure the distance of objects in space?

Measuring the distance of objects in space is difficult because of the vast distances involved. Light travels at a finite speed, so the farther an object is, the longer it takes for its light to reach us. This means that we are seeing objects as they were in the past, and their current distance may have changed since then due to their motion or expansion of the universe. Additionally, objects in space can be very faint and require sophisticated instruments to detect and measure their distance.

3. How do we use the concept of parallax to measure the distance of objects?

Parallax is used to measure the distance of objects by comparing their apparent shift in position when viewed from different points on Earth's orbit around the Sun. The smaller the parallax angle, the farther away the object is. This method is commonly used for determining the distance of nearby stars and planets.

4. What is redshift and how is it used to measure distances in space?

Redshift is a phenomenon where an object's light appears to shift towards the red end of the spectrum due to its motion away from us. This is due to the Doppler effect, where the wavelength of light is stretched as the source moves away from the observer. The amount of redshift can be used to determine an object's velocity and, in turn, its distance based on the expansion of the universe.

5. What are standard candles and how are they used to measure distances in space?

Standard candles are objects with known luminosity, such as certain types of stars, which can be used to estimate distance based on their apparent brightness. By comparing the known luminosity of a standard candle to its apparent brightness, we can calculate its distance using the inverse square law. This method is commonly used for measuring the distance of objects in the far reaches of the universe.

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