Chapter 23, Problem 92GP

To determine

Distance of original object from the left lens.

Answer to Problem 92GP

Solution: 50 cm:

Explanation of Solution

Image formed by left lens will be as object for right lens. And image formed by right lens would be the final image.

Given:

Focal length of left lens f_L = 15 cm

Focal length of right lens f_R = 20 cm

Distance between both the lenses is = 30 cm

Final image is halfway between the lenses and that will be image formed by right lens,

So, for right lens, v = -15cm (because image is behind the lens)

Formula used:

Lens formula for focal length, $1/f=1/v–1/u$

Calculation:

For the right lens

$v=-\text{15}\text{cm},f_R=\text{ 2}0\text{cm}$

$\begin{array}{l}1/f_R=1/v–1/u\hfill \\ 1/20=1/\left(-15\right)–1/u\hfill \\ 1/u=-1/15–1/20=-\left(4+3\right)/60=-7/60\hfill \\ u=-6\text{0/7 cm}\hfill \end{array}$

Now image distance for left lens would be = 30 – (60/7)=150/7 cm

So, for left lens $v=\text{ 15}0/\text{7 cm},f_L=\text{ 15 cm}$

$\begin{array}{l}1/f_L=1/v-1/u\hfill \\ 1/15 =1/\left(150/7\right)–1/u\hfill \\ 1/u=7/150–1/15=-3/150=-1/50\hfill \\ u=-5\text{0 cm}\hfill \end{array}$

Object is at 50 cm in the left of left lens.