Question

A converging lens with a focal length of 60 cm and a diverging lens with a focal length of -70 cm are 310 cm apart. A 2.7-cm-tall object is 80 cm in front of the converging lens.

Calculate the distance between the final image and the diverging lens.

Express your answer to two significant figures and include the appropriate units.

Calculate the image height.

Express your answer to two significant figures and include the appropriate units.

Answer 1

For Converging lens using lens equation:

1/f = 1/u + 1/v

u = object distance = 80 cm

v = image distance = ?

f = focal length = 60 cm

1/v = 1/f - 1/u

1/v = 1/60 - 1/80

v = 80*60/(80 - 60) = 240 cm

Image of converging lens will be 240 cm right of converging lens, Now this image will work as object for diverging lens, So for diverging lens object distance will be

u1 = 310 - 240 = 70 cm

f1 = -70 cm

v1 = ?

1/v1 = 1/f1 - 1/u1

1/v1 = -1/70 - 1/70

v1 = -70/2 = -35 cm (-ve sign means image will be left of diverging lens)

distance between final image and diverging lens = 35 cm

Part B

Magnification will be

M = M1*M2 = (-v/u)*(-v1/u1)

M = (-70/80)*(-(-35)/70)

M = -35/80 = -7/16 = -0.4375

Now we know that

M = hi/ho = -0.4375

hi = image height = ?

hi = ho*(-0.4375)

hi = 2.7*(-0.4375) = -1.18

Image height = 1.18 cm

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