An object is located 4cm from the first of two thin converging lenses of focal lengths 2m and 1m. Respectively. The lenses are separated by 3m. The final image formed by the second lens is located from the source at a distance of

Options

A. 8M
B. 5.5m
C. 6m
D. 6.5

Answer

B

Explanation

From the lens formula (for first lens).
`(1)/(f_(1))=(1)/(v_(1))=(1)/mu_(1) Rightarrow (1)/(2)=(1)/(V_(1))-(1)/(-4)`
`Rightarrow (1)/(2)+(1)/(4)=(1)/(v_(1))=(3)/(4)`
`v_(1)=(4)/(3), mu_(2)=3-(4)/(3)=5//3` The image will be treated as the source for second lens, then again from lens formula, we have
`(1)/(f_(2))=(1)/(v_(2))-(1)/(u_(2))Rightarrow (1)/(1)+5//3 ...(ii)`
`Rightarrow 1-5//3=(1)/(v_(2)) Rightarrow v_(2)=-3//2`
This is the final image distace from the primary source (or object).
Then, d=4+3-1.5=5.5