A pencil of height 1cm is placed 30cm from an equiconvex lens, refractive index `n=3//2` , radius of curvature for both the surfaces, `R_(1)=R_(2)=R=10 cm`
Find the location of the image and descrive characteristics.

Explanation

The rays of light divergre from the object , it is a real object. Focal length of a convex lens is positive.
` (1)/(f)=(n_(2)-n_(1))/(n_(1))((2)/(R))=((3//2)-1)/(1)((2)/(10))=(1)/(10)`
The given parameters are
` u=-30 cm` and `f=+10 cm`
Substituting these values in thin-lens equation, we have
`(1)/(v)-(1)/(u) =(1)/(f)rArr (1)/(v)-(1)/((-30))=(1)/(10)`
which on solving gives `v=+15cm`.
The image distance is positive, which implies that the image is real. The lateral magnification is
`m=(v)/(u)=(15)/((-30)) =-(1)/(2)`
The image is half the size of the object, size of the image is `0.50` cm . The negative sign with magnification shows inverted image.