# Problem: A converging lens with a focal length of 40 cm and a diverging lens with a focal length of -40 cm are 160 cm apart. A 1.0-cm-tall object is 60 cm in front of the converging lens.a) Calculate the image position in front of the second lensb) Calculate the image height.

###### FREE Expert Solution

Lens maker equation:

$\overline{)\frac{\mathbf{1}}{{\mathbf{s}}_{\mathbf{o}}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{s}}_{\mathbf{i}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{f}}}$

Magnification;

$\overline{){\mathbf{m}}{\mathbf{=}}\frac{\mathbf{-}{\mathbf{s}}_{\mathbf{i}}}{{\mathbf{s}}_{\mathbf{o}}}{\mathbf{=}}\frac{{\mathbf{h}}_{\mathbf{i}}}{{\mathbf{h}}_{\mathbf{o}}}}$

a)

For the converging lens:

1/60 + 1/si = 1/40

1/si = 1/40 - 1/60 = 1/120

si = 120 cm

This image distance is the object distance for the diverging lens, which is now 40cm in front of the lens. This is because the lenses are 160cm apart.

Therefore:

1/140 + 1/si = 1/-40

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###### Problem Details

A converging lens with a focal length of 40 cm and a diverging lens with a focal length of -40 cm are 160 cm apart. A 1.0-cm-tall object is 60 cm in front of the converging lens.

a) Calculate the image position in front of the second lens

b) Calculate the image height.