Question

Maggie needs to determine the diameter of the wire used to make the filament of an incandescent lightbulb. She decides to project a magnified image of the filament onto a screen using a lens. Describe Maggie's experimental setup in words.

Answer 1

If the focal length of the lens used by Maggie be f, distance of the bulb from the lens, i.e., object distance be u, and distance of the screen from the lens, i.e., image distance be v, then, we know,

1 / f = 1 / v - 1 / u.

Which gives : u = vf / ( f - v ).

Using the equation, the position of the filament inside the bulb can be determined.

Now, magnification of the image formed on the screen = m = v / u.

If the measured diameter of the image wire on the screen be d_i,

then, actual diameter of the bulb = d_o is given by :

m = d_i / d_o

or, d_o = d_i / m.

Thus, the diameter of the incandescent lightbulb can be determined.