CALCULUS

If you could give an explenation with the answers, that'd be wonderful so I actually know how to solve similar problems in the future. :) Thank you so much!

1. A convex lens with focal length f centimeters will project the image of an object on a point behind the lens. If an object is placed a distance of p centimeters from the lens, then the distance q centimeters of the image from the lens is related to p and f by the lens equation: 1/p + 1/q = 1/f

A. If the focal length of the convex lens is supposed to be 5 cm, and if the image is formed 7 cm from the lens, find the distance, p, from the lens to the object. (It’s not necessary to simplify your answer.)

B. Find an expression that gives q as a function of p, assuming that the focal length is a constant of 5 centimeters.

C. Sketch a graph of q as a function of p (i.e., q(p)), assuming that the focal length is a constant of
5 centimeters. Show any important features of the graph.

D. Find lim p->infinity q(p) and lim p->5+ q(p). What do these limits represent physically? What must happen to the distance of the image and the object?

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  1. You have the equation -- just plug in the numbers.

    1/p + 1/7 = 1/5
    1/p = 1/5 - 1/7
    1/p = 2/35
    p = 35/2

    1/p + 1/q = 1/5
    1/q = 1/5 - 1/p
    1/q = (p-5)/5p
    q = 5p/(p-5)

    The above is just algebra I, you know.

    any online graphing site can do this. Try wolframalpha.com

    limit as p->infinity = 5
    limit as p->5 = infinity
    parallel rays converge to the focal length (their origin is at infinity)

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