Graphing conves lense relationships to find focal lenght with slope

[pices_zodiac]

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)

 

[rl.bhat]

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.

 

[kerimek]

which is not the slope

I would suggest approaching this problem by first understanding the concept of focal length and its relationship to object-lens distance and image-lens distance. Focal length is defined as the distance between the center of a lens and its focal point, where parallel rays of light converge to a single point. This distance is constant for a given lens and is a key factor in determining the magnification and clarity of an image.

To graph the relationship between object-lens distance and image-lens distance, you can plot the values for u (object-lens distance) on the x-axis and v (image-lens distance) on the y-axis. The resulting graph should show a linear relationship between the two variables. However, the slope of this line will not directly represent the focal length.

To find the focal length using the graph, you can use the equation 1/u + 1/v = 1/f. Rearranging this equation to solve for f, you get f = uv/(u+v). This means that the value of f can be determined by finding the product of u and v, and then dividing it by the sum of u and v. This calculation can be done for any point on the graph, and the resulting value will represent the focal length for that specific object-lens and image-lens distance.

In terms of your desired equation of y=mx+b, it is important to note that in this case, the slope (m) would not represent the focal length, but rather the inverse of the focal length (1/f). This is because as u increases, v decreases, and vice versa, resulting in a negative slope. However, the y-intercept (b) would still be 0, as it represents the point where the line intersects the y-axis when u=0.

In conclusion, while the slope of the graph does not directly represent the focal length, it can still be used to determine the focal length using the equation 1/u + 1/v = 1/f. I hope this explanation helps you better understand the relationship between object-lens distance, image-lens distance, and focal length.