[Q] Do you understand what is numerical aperture and f number?

[good_phy]

Hi, I studied concept of numerical aperture and f number

I learned numerical aperture(N.A) is measure of how much light can be entered into the

optical system, its mathematical expression is N.A = $$nsin\theta_m$$ where n is

index of refraction of immersing medium surrounding lens and $$\theta_m$$ is

maximum angle between optical axis and rim of lens.


I got a question. What is the point from which two line(one is from the point to rim of lens,

another is from the point along optical axis to lens) make maximum angle?


I think maximum angle is varying as the point moves along axis, So it is not clear for me.


And why can more light enter the optical system if n increases, causes N.A increase.


Please solve my question.

 

[Andy Resnick]

I'm not sure I understand your question, but the cone angle used in the definition of NA has the apex located at the focal plane of the lens, not arbitrarily located along the optical axis.

Does that help?

 

[sir-pinski]

Hi there, it sounds like you have a good understanding of numerical aperture and f number. To answer your question, the point from which the two lines make the maximum angle is the point on the object being viewed that is closest to the lens. As you mentioned, the maximum angle will vary as the point moves along the axis, but it will always be measured from the closest point on the object to the lens.

As for why more light can enter the optical system when n increases, this is because the index of refraction is a measure of how much the light is bent as it passes through a medium. When the index of refraction increases, the light is bent more and therefore can enter the optical system at a greater angle, resulting in a higher numerical aperture.

I hope this helps to clarify your questions. Keep studying and learning, and you'll continue to deepen your understanding of these concepts.