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How to determine focal length from the equation f = racL2 − d24L using a graph?

Physics

ScanSolve AI Answer

Step-by-step solution

2 steps

To determine the focal length ff using a graph, we need to linearize the given equation f=L2−d24Lf = \frac{L^2 - d^2}{4L} into the form Y=mX+CY = mX + C.

  1. Rearrange the equation.

    Multiply both sides by 4L4L:

    4Lf=L2−d24Lf = L^2 - d^2

  2. Identify variables for plotting.

    To obtain a linear graph Y=mX+CY = mX + C, we can set:
    Y=L2−d2Y = L^2 - d^2
    X=4LX = 4L
    The equation then becomes:

    Y=fXY = fX

    This is a linear equation where the y-intercept C=0C=0 and the slope mm

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