Question

A microscope consists of a convergent objective with focal length 15 mm and a convergent eyepiece with a focal length of 60 mm separated by a fixed distance of 80 cm. What is the total magnification achieved when observing an ant at a distance of 44 mm from the objective?

Lens 1 Lens 2 2.5 cm 4 cm 10 cm

Answer 1

here,

for the objective lens

the focal length , f1 = 15 mm = 1.5 cm

the object distance , do1 = - 44 cm = 4.4 cm

let the image distance be di2

using the lens formula

1/f1 = 1/di1 - 1/do1

1/1.5 = 1/di1 - 1/(- 4.4)

solving for di1

di1 = 2.28 cm

for the eyepiece lens

the focal length , f2 = 60 mm = 6 cm

the object distance , do2 = - (80 - di1 ) cm = - 77.72 cm

let the image distance be di2

using the lens formula

1/f2 = 1/di2 - 1/do2

1/( 6) = 1/di2 - 1/(- 77.2)

solving for di2

di2 = 6.51 cm

the overall magnification , m = (di2/di2) * ( di1 /do1)

m = (6.51 /(- 77.72)) * (2.28 /(- 4.4))

m =

the overall magnification is 0.043