Stuck on math in deriving an optics equation

AI Thread Summary
The discussion revolves around deriving the formula for bright fringes in optics, with a focus on a specific mathematical approximation. The user is struggling with the expression (1+a)1/2 and seeks clarification on simplifying it to 1+a/2 when a is much smaller than 1. Examples provided demonstrate this approximation using small values of a, showing that the results are close to the expected values. The user expresses concern about the triviality of the question but is seeking assistance to move forward with their project. The conversation highlights the importance of understanding mathematical approximations in physics.
Puchinita5
Messages
178
Reaction score
0

Homework Statement



Hi. For a project I have to derive this formula for bright fringes in optics, but I'm stuck on this simple math part (or maybe its not so simple)...ive attached a picture of where i don't understand...it might be considered a simple math problem so I'm sorry if this is too trivial a question for physics forums :)

Homework Equations





The Attempt at a Solution

 

Attachments

  • question pf.jpg
    question pf.jpg
    13.9 KB · Views: 426
Physics news on Phys.org
(1+a)1/2 can be approximated by 1+a/2 if a<<1.

For example:

a=0.02: 1.021/2=1.00995...~1.01,

a=0.002: 1.0021/2=1.0009995...~1.001

ehild
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Unclear geometry in optics problem
Replies
1
Views
1K
Incident Angle Limitation Derivation in Optical Fibre
Replies
5
Views
2K
Diffraction Grating - Calculating Ruling Width
Replies
2
Views
1K
Algebra: How do I derive this equation given two other equations?
Replies
2
Views
2K
How does the sign convention work in ray optics?
Replies
6
Views
4K
How do you Calculate Ampacity of a Conductor Geometry?
2
Replies
64
Views
5K
An ambigious optical system with ambigious solutions [JEE Adv - 20`16]
Replies
19
Views
2K
How Do Spring Length Calculations Relate to Frequency and Harmonics?
Replies
25
Views
3K
Optics: Solving for Slit Size Missing Fringes
Replies
1
Views
1K
Active Galaxies: Comparing Optical and Radio Astronomers' Perspectives
Replies
10
Views
2K

Hot Threads

Recent Insights

Back
Top