Understanding Spatial Resolution: Calculating and Applying θmin=1.22λ/D

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Homework Help Overview

The discussion revolves around the concept of spatial resolution in optics, specifically in relation to the formula θmin=1.22λ/D. Participants are exploring the calculation of spatial resolution and its relationship to angular resolution.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to calculate spatial resolution using the provided formula and questioning the appropriate units for the answer. There is discussion about the relationship between spatial resolution and angular resolution, with some participants exploring the implications of arc length in relation to angle.

Discussion Status

The discussion is ongoing, with participants providing insights into the relationship between spatial and angular resolution. There is a recognition of the need to clarify the meaning of certain variables, such as the radius in the context of the arc length formula.

Contextual Notes

Participants are navigating potential confusion regarding units of measurement and the definitions of terms related to spatial resolution. The specific context of the problem includes assumptions about the geometry of lenses and focal planes.

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Homework Statement


擷取1.PNG


Homework Equations


θmin=1.22λ/D

The Attempt at a Solution


(a)θmin=1.22λ/D
(b)θs=1.22(600nm)/30mm=24.4μm but what is spatial resolution and how to calculate it??
 
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kenok1216 said:

Homework Statement


View attachment 99604

Homework Equations


θmin=1.22λ/D

The Attempt at a Solution


(a)θmin=1.22λ/D
(b)θs=1.22(600nm)/30mm=24.4μm but what is spatial resolution and how to calculate it??
That answer should be in units appropriate for an angle, certainly not μm .
 
kenok1216 said:
what is spatial resolution and how to calculate it??
It's related to the angular resolution. You can think of the spatial resolution as the arc length of a circle subtended by the angle of angular resolution.
 
SammyS said:
That answer should be in units appropriate for an angle, certainly not μm .
sor, it is μrad
 
kenok1216 said:
sor, it is μrad
Yes.
 
blue_leaf77 said:
It's related to the angular resolution. You can think of the spatial resolution as the arc length of a circle subtended by the angle of angular resolution.
s=rθ, so what is r is this question?object distance? focal length?image distance?
 
kenok1216 said:
s=rθ, so what is r is this question?object distance? focal length?image distance?
About the circle I was talking about, you can assume it to be centered at the center of the lens and since your image is located at the focal plane, the arc length of interest must touch the focal plane. What will r be?
 
blue_leaf77 said:
About the circle I was talking about, you can assume it to be centered at the center of the lens and since your image is located at the focal plane, the arc length of interest must touch the focal plane. What will r be?
Focal lenght?
 
kenok1216 said:
Focal lenght?
Yes.
 
  • #10
SammyS said:
Yes.
Thank
 

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