Question

an object is placed 15.8 cm in front of a thin converging lens with an unknown focal length. if a real image forms behind the lens with an image distance of 4.2cm what is the focal length of the lens

Answer 1

On what:

f (is the focal length of the lens) = ?
p (is the distance from the object to the lens) =15.8 cm
p' (is the distance from the image to the spherical lens) = 4.2 cm

Using the Gaussian equation, to know where the object is situated (distance from the point).


`(1)/(f) = (1)/(p) + (1)/(p')`

`(1)/(f) = (1)/(15.8) + (1)/(4.2)`

`(1)/(f) = (2.1)/(33.18) + (7.9)/(33.18)`

`(1)/(f) = (10)/(33.18)`
Product of extremes equals product of means:

`10*f = 1*33.18`

`10f = 33.18`

`f = (33.18)/(10)`

`\boxed{\boxed{f = 3.318\:cm}}\end{array}}\qquad\quad\checkmark`