What is the formula for determining small angles in spherical diopters?

[duchuy]

Homework Statement

I can't seem to understand the relation

Relevant Equations

angle = length / length

Hi,
I don't understand how the professor managed to determine the values of alpha, alpha' and omega. What is the formula tha´t is applied to determine alpha = SP / AS and so on... knowing that alpha is a really small angle. Cheers

 

[hutchphd]

You need to ask specific questions one at a time as you try to work through this. You could start by saying in specific detail what you wish to know when we are finished here.
The typical way to define an angle (in radians) is ?

 

[duchuy]

You need to ask specific questions one at a time as you try to work through this. You could start by saying in specific detail what you wish to know when we are finished here.

Thanks for your reply, would you then mind explaining me how the professor managed to determine that alpha = SP / AS? I did try to use trigonometric formulas for this but the results were nowhere near SP / AS. Thanks a lot.

 

[hutchphd]

Define an angle (in radians) http://www.learnAlberta.ca/content/...adian is the measure,the radius of the circle.

 

[duchuy]

Define an angle (in radians) http://www.learnAlberta.ca/content/memg/Division04/Radian Measure/index.html#:~:text=Radian measure is the ratio,of the arc (r).&text=One radian is the measure,the radius of the circle.

I don't really understand... PAC which is the alpha angle doesn't have A as the center of the circle and SP is the length of the the straight line SP not the curvature SP. Or in this case is SP referring to the length of the curvature? That would make sense for the omega angle but still not for alpha no?
Thanks

 

[hutchphd]

I see. Does he specify pt A in some way or is it arbitrary? This may be an approximation.

 

[duchuy]

So when you say that this may be an approximation, are you saying that since alpha is a really small angle, therefore you could write tan alpha = alpha then use the tan = o/a to write these expressions right? This makes a lot of sense thanks a lot!