Graphing conves lense relationships to find focal lenght with slope

Click For Summary
SUMMARY

The discussion focuses on graphing the relationship between object-lens distance (u) and image-lens distance (v) for a converging lens to determine the focal length (f) as the slope of the graph. The lens equation, 1/u + 1/v = 1/f, is utilized to derive the relationship. By plotting 1/u against 1/v, a straight line is produced with a slope of -1, where the x and y-axis intercepts correspond to 1/f. This method effectively allows for the calculation of the focal length from the graph.

PREREQUISITES
  • Understanding of the lens equation: 1/u + 1/v = 1/f
  • Basic knowledge of graphing linear equations in the form y = mx + b
  • Familiarity with the concept of slopes and intercepts in coordinate geometry
  • Ability to manipulate algebraic equations for lens calculations
NEXT STEPS
  • Explore the derivation of the lens equation and its applications in optics
  • Learn about graphing techniques for linear relationships in physics
  • Investigate the significance of focal length in different types of lenses
  • Study the impact of varying object-lens and image-lens distances on focal length calculations
USEFUL FOR

Students studying optics, physics educators, and anyone interested in understanding the mathematical relationships in lens systems.

pices_zodiac
Messages
1
Reaction score
0

Homework Statement


I need to find the relationship between object-lens distance and image-lens distance for a lense(converging) but cannot graph the relationship in a way that the focal length is the slope for the graph



Homework Equations


1/u + 1/v = 1/f
where u= object lense distance and v= image lense distance and f= focal lenght

y=mx+b --> I would like m=focal length and b=0


The Attempt at a Solution


so far, I can only come up with:
-u ( 1/[uv]) = -1/v
thus ( 1/[uv]) is the slope.. but f= (v+u)/(uv)
 
Physics news on Phys.org
You can write the lens equation as
(1/u)/(1/f) + (1/v)/(1/f) = 1.
It is in the form of
x/a + y/b = 1.

Draw the graph 1/u vs 1/v. You will get a straight line with slope (-1). The intercept on x and y-axis are equal and it is equal to 1/f.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
4
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
1
Views
2K
Replies
3
Views
3K
  • · Replies 12 ·
Replies
12
Views
5K
  • · Replies 20 ·
Replies
20
Views
4K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 16 ·
Replies
16
Views
3K