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.

a)Given for a concave lens, 

    Focal length of the lens, $\mathrm{f}=-15 \mathrm{cm}$

    Distance of image from lens, $\mathrm{v}=-10 \mathrm{cm}$

    Distance of object in front of lens, $\mathrm{u}=?$

    From lens formula:

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

    Substituting values,

                                                   $\frac{1}{-10}-\frac{1}{\mathrm{u}}=\frac{1}{-15}$

    On simplifying,

                                                       $\mathrm{u} = -30 \mathrm{cm}$

   Thus, the object is at a distance of 30cm from the lens.

b)The ray diagram is as shown below,