How to Apply L'Hopital's Rule to Probability Equations?

[Crazy Gnome]

The problem statement

Using the Equation

P(\theta)= P₁[ \frac{sin(Nkdsin(\theta)/2)}{sin(kdsin(\theta)/2)} ]²

show that the probability at sin(\theta)=j\frac{\lambda}{d}, where j is an integer, is P(\theta=sin^-1(j\lambda/d))=N²P₁

Hit: find \frac{sin(Nkdsin(\theta)/2)}{sin(kdsin(\theta)/2} as sin(\theta) approaches j(\lambda/d) using L' Hopital's rule.



My problem: I am not sure how to apply L Hopital's rule to this situation. What would be my F(x) and what would be my G(x)?

 

[badphysicist]

This looks like a problem from diffraction theory, but here's a little help. Basically L'Hopital's rule is used when the limit as an equation that can be expressed as a fraction of two equations diverges. L'Hopital's rule says to find the limit of the derivative of the numerator over the derivative of the denominator.

 

[tiny-tim]

I am not sure how to apply L Hopital's rule to this situation. What would be my F(x) and what would be my G(x)?

Hi Crazy Gnome!

Your x can be either θ or sinθ …

it makes no difference, the result will be the same.

(Personally, I'd use θ. )