Radius of curvature of a biconvex lens is 20 cm. An object of 2 cm height is placed at 30 cm from lens, then which option represents the image ?

Options

A. Virtual, erect, of height 1 cm
B. Virtual, erect, of height 0.5 cm.
C. Real, inverted, of height 4 cm.
D. Real, inverted, of height 1 cm.

Answer

A, C, D

Explanation

R=20 cm, `h_0`=2 cm , u=-30 cm
Now `1/f=(mu-1)((1)/(R_1)-(1)/(R_2))`
`=(3/2-1)[(1)/(20)-(-(1)/(20))]`
`1/f=(3/2-1)xx(2)/(20)`
`therefore f=20` cm
Also,`1/f=1/v-1/u`
`therefore(1)/(20)=1/v+(1)/(30)`
`therefore 1/v=(1)/(20)-(1)/(30)`
`=(10)/(600)`
`therefore v=60` cm
`m=(h_1)/(h_0)-v/u`
`therefore h_i=v/uxxh_0`
`=(60)/(30)xx2`
`therefore h_i=-4` cm
negative sign represents that the image is inverted