Question

A bright object and a viewing screen are
separated by a distance of 76.0 cm. At what
location(s) between the object and the
screen should a lens of focal length 16.0 cm
be placed in order to produce a crisp image
on the screen?
42.9 cm
22.9 cm
32.9 cm
52.9 cm​

Answer 1

Answer:

Let the distance from lens to object be "p"  

Let the distance from lens to screen be "q".

If "f" is the focal length 11 cm ,then the lens eq. is;

(1/p) + (1/q) = (1/f)

You are also told that the sum of "p" & "q" is a fixed L = 66 cm;

p + q = L

eliminate "q" from these two eqs, by direct substitution to get;

(1/p) + (1/L-p) = 1/f

multiply both sides by p(L-p)f to get;

(L-p)f + pf = p(L-p)

simplify and write in standard quadratic form;

p^2 - Lp + Lf = 0

solve this using the quadratic eq.

The two solns. I get are;

nearest; p = 14cm

farthest; p = 52 cm

Explanation:

simple science!! liked helping you!!