Question

Focal length of a concave lens is -7.50 cm , at what distance should an object be placed so that its image is formed 3.70 cm from the lens?

Answer 1

On what: 

f (is the focal length of the lens) = - 7.50 cm 
p (is the distance from the object to the lens) = ?
p' (is the distance from the image to the spherical lens) = 3.70 cm

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

$\frac{1}{f} = \frac{1}{p} + \frac{1}{p'}$
$\frac{1}{-7.50} = \frac{1}{p} + \frac{1}{3.70}$
$\frac{1}{p} = - \frac{1}{7.50} - \frac{1}{3.70}$
$\frac{1}{p} = \frac{-3.70-7.50}{27.75}$
$\frac{1}{p} = \frac{- 11.20}{27.75}$
Product of extremes equals product of means:
$- 11.20*p = 1*27.75$
$- 11.20p = 27.75\:simplify\:by*(-1)$
$11.20p = - 27.75$
$p = \frac{-27.75}{11.20}$
$\boxed{\boxed{p \approx -2.47\:cm}}\end{array}}\qquad\quad\checkmark$