Solve Optics Problem: Diameter of Star Imaged w/ 18" Telescope

In summary, the conversation discusses the calculation of the diameter of a star imaged in the focal plane of a telescope, using lens diffraction theory and the equation for diffraction at a circular aperture. The solution involves multiplying 1.22 by the wavelength and dividing by the aperture diameter to determine the half angular width of the central maximum.
  • #1
eluru
2
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Optics Problem( pleasez help me)

Consider a telescope with an aperture of 18 inches and focal length of 120 inches.
what is the diameter of the star imaged in focal plane of telescope? Take the image diameter to be associated with the first minimum in the diffraction pattern of the image. Use wavelength of 550nm.

Hint: By Using lens diffraction theory.
 
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  • #2


What is the equation for diffraction at a circular aperture?
 
  • #3


hiiiiiiii friend.,

for the circular aperture

U= C exp(ikr) * integral of Exp(ikysin@) 2sqrt(R^2-Y^2) dy
bet ween the limits (-R,R)
 
Last edited:
  • #4


The nice Mr Rayleigh solved it for you
 
  • #5


In other words 1.22 times wavelength divided by aperture diameter for the half angular width of the central maxima.
 

1. What is the formula for calculating the diameter of a star imaged with an 18" telescope?

The formula for calculating the diameter of a star imaged with an 18" telescope is: D = 2 * f * tan(θ), where D is the diameter of the star, f is the focal length of the telescope, and θ is the angular size of the star.

2. How do I determine the focal length of my 18" telescope?

The focal length of a telescope can usually be found in the manufacturer's specifications or by measuring the distance from the lens or mirror to the focal point. If this information is not available, you can also calculate the focal length by measuring the distance between the lens/mirror and the eyepiece, and then adding the diameter of the eyepiece.

3. What is the angular size of a star and how is it measured?

The angular size of a star is the apparent size of the star as seen from Earth. It is measured in degrees, minutes, and seconds of arc. This can be calculated using the formula θ = D/d, where θ is the angular size, D is the diameter of the star, and d is the distance from Earth to the star.

4. Does the diameter of the telescope affect the diameter of the star imaged?

Yes, the diameter of the telescope does affect the diameter of the star imaged. A larger diameter telescope allows for more light to enter, resulting in a clearer and more detailed image of the star with a larger diameter. However, other factors such as atmospheric conditions and the quality of the telescope's optics can also impact the final image.

5. Are there any limitations to using an 18" telescope for imaging stars?

While an 18" telescope can produce high-quality images of stars, there are some limitations to consider. For example, light pollution and atmospheric conditions can affect the clarity of the image. Additionally, using a longer focal length eyepiece can help to magnify the image, but it may also result in a smaller field of view. It is important to consider these factors when choosing the appropriate telescope for your desired viewing or imaging goals.

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