A biconvex lens has a radius of curvature of magnitude `20cm`. Which one of the following options describes best the image formed of an object of height `2cm` place `30 cm` from the lens ?

Options

A. Virtual, upright, height = 1 cm
B. Virtual, upright, height = 0.5 cm
C. Real, inverted, height = 4 cm
D. Real, inverted, height 1 cm.

Answer

C

Explanation

`(1)/(f)=(mu-1)((1)/(R_(1))-(1)/(R_(2)))`
`rArr" "(1)/(f)=(1.5-1)((1)/(20)-(1)/(-20))`
`rArr" "f=20cm`
Using lens formula :
`(1)/(f)=(1)/(v)-(1)/(u)`
`rArr" "(1)/(20)=(1)/(v)-(1)/(-30)`
`rArr" "(1)/(v)=(1)/(20)-(1)/(30)=(3-2)/(60)`
`v=60cm`.
Hence image is real.
Magnification
`m=(h_(2))/(h_(1))=(v)/(u)`
`rArr" "(h_(2))/(2)=(60)/(-30)rArr h_(2)=-4cm`
Image is real and 4 cm in height and inverted.