Optic axis of a thin equi-convex lens is the x-axis. The co-ordinates of a point object and its image are `(-40 cm,1 cm) and (50 cm,-2 cm),` respectively. Lens is located at

Options

A. `x=+20 cm`
B. `x=-30cm`
C. `x=-10 cm`
D. origin

Answer

C

Explanation

Linear magnification `m=(-2cm)/(1 cm)=-2`
`i.e.,` image is real and inverted.
`|v|=2|u|`
Let `|u|=x` then `|v|=2x`
now `|u|+|v|=50-(-40)=90`
`:. x+2x=90`
or `x=30cm`
Hence, distance of object from the lens is `30 cm` and of object is `60cm`. therefore, lens should be located at `x=-10cm` as shown in figure.