Question

Given x=1/u
y=1/v
and. z=1/f
where u, vand f stand for object distance,
image distance and focal length for a lens.
What is the nature of graph between y
versus x? What is the slope of the graph?​

Answer 1

Given:

x = 1/u , y = 1/v and z = 1/f , where u is object distance, v is image distance and f is focal length of the lens.

To find:

• Nature of graph between y and x.

• Slope of the graph

Calculation:

Applying Lens Formula , we get :

$\rm{ \therefore \: \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} }$

Rearranging the equation:

$\rm{ = > \: \dfrac{1}{v} = \dfrac{1}{u} + \dfrac{1}{f} }$

$\rm{ = > \: y = x + z }$

Comparing this equation with standard linear equation :

$\boxed{ \bold{y = mx + c}}$

For convex lens, we shall put negative values of u and get positive values of v. Also f always has positive value for Convex lens.

Hence a linear graph will be obtained in the 2nd Quadrant with positive slope and positive intercept.

Slope of the graph is 1 , i.e. the graph is at angle of 45° with horizontal.