Two lenses A and B having focal lengths 2.0 cm and 5.0 cm, respectively are placed 14 cm apart. Lens A is placed to the left of lens B. An object is placed 3 cm to the left of lens A. The distance of the image from lens A will be

Options

A. `40/3 cm`
B. `82/3 cm`
C. `112/5 cm`
D. `92/5 cm`

Answer

B

Explanation

Focal length of lens A, `f_1 = 2 cm ` focal length lens `B_1, f_2 = 5cm`


The given situation is shown is the figure. For lens A
` u_1 = - 3 cm , v_1 = ? `
From lens formula ,` 1/v - 1/u = 1/f`
` (1)/(v_1) + 1/3 = 1/2`
`rArr v_1 = 6 cm `
Image formed by lens A works as a object for lens B.
Hence, for lens B
`u_2 = - (14 - 6) = - 8 cm `
From lens formula
` (1)/(v_2) - (1)/(u_2) = (1)/(f_2)`
` (1)/(v_2) + (1)/(8) = 1/5`
` rArr (1)/(v_2) = 3/40`
` therefore v_2 = 40/3 cm`
` therefore ` Distance of final image (A'' B'') from lens A ,
` = 14 + v_2 = 14 + 40/3 = 82/3 cm `