Question

A 13.51 cm high object is placed 530 mm in front of two converging lenses separated by 317 mm. The focal length of the first converging lens has a magnitude 611 mm. The focal length of the second converging lens has a magnitude 512 mm.
Find the location of the image relative to the second lens.
i2 =  mm
Find the magnificationj of the lens system.
M =  
Find the height of the lens system image.
hi =  mm

Answer 1

here,

height of object , ho = 13.51 cm

for the first lens

focal length , f1 = 611 mm = 61.1 cm

the object distance , do1 = 530 mm = 53 cm

let the image distance be di1

using the lens formula

1/di1 + 1/do1 = 1/f1

1/di1 + 1/53 = 1/61.1

solving for di1

di1 = - 400 cm

for the seccond lens

focal length , f2 = 512 mm

the object distance , do1 = 317 mm - ( - 4000) mm = 4317 mm

let the image distance be di2

using the lens formula

1/di2 + 1/do2 = 1/f2

1/di2 + 1/4317 = 1/512

solving for di2

di2 = 580 mm

the final image is 580 mm from the seccond lens

b)

magnification , m = ( di1/do1) *(di2/do2)

m = (- 4000 /530) * ( 580/4317)

m = - 1.02

c)

the height of the lens system image , hi = m ( ho)

hi = - 13.72 cm

hi = - 137.2 m