An object is placed at a distance of 12 cm from a convex lens on its principal axis and a virtual image of certain size is formed. If the object is moved 8 cm away from the lens, a real image of the same size as that of the virtual image is formed. The focal length of the lens in cm is

Options

A. 15
B. 16
C. 18
D. 19

Answer

B

Explanation

`(1)/(v_1)-(1)/(-12)=(1)/(f)implies(1)/(v_1)=(1)/(f)-(1)/(12)=(12-f)/(12f)`
`v_1=(12f)/(12-f)`
`m_1=(I)/(O)=(v_1)/(u)=(12f)/((12-f)(-12))-(f)/((12-f))`
`(1)/(v_2)-(1)/(-20)=(1)/(f)implies(1)/(v_2)=(1)/(f)-(1)/(20)=(20-f)/(20f)`
`v_2=(20f)/(20-f)`
`m_2=(I)/(O)=(v_2)/(u)=(20f)/((20-f)(-20))=-(f)/((20-f))`
`m_1=-mu_2`
`-(f)/(12-f)=(f)/(20-f)implies-20+f=12-f`
`f=16cm`