A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.

Given, a concave lens. 

Focal length, f = - 15 cm
Image distance, v = - 10 cm [Concave lens forms virtual image on same side as the object, so v is - ve] 

Using the lens formula,

                          $\frac{1}{\mathrm{f}} = \frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}$ 

$\Rightarrow$                     $$\begin{gathered} \frac{1}{\mathrm{u}} = \frac{1}{\mathrm{v}}-\frac{1}{\mathrm{f}} \\ = \frac{1}{-10}-\frac{1}{-15} \\ = \frac{-3+2}{30} \\ =-\frac{1}{30} \end{gathered}$$ 

Therefore,
Object is placed at a distance of 30 cm ( negative) from the lens. 

The ray diagram is as shown below:  


 

AB is the position of the object.