Skip to content

Two lens system - Image distance and magnification

Home arrow Problems and Answers arrow Optics arrow Two lens system - Image distance and magnification


Two lens system - Image distance and magnification E-mail
User Rating: / 0
PoorBest 
Two converging lenses, with the focal length f1 = 10 cm and f2 = 15 cm are placed 40 cm apart, as shown on the figure. An object is placed 60 cm in front of the first lens as show in second figure.
a) Find the position of the final image formed by the combination of the two lenses?
b) Find magnification of the final image formed by the combination of the two lenses?
 
Optics - Find image distance and magnification for two lens system Optics - Find image distance and magnification for two lens system - Physics Problems
Two converging lenses, with the focal length f1 = 10 cm and f2 = 15 cm are placed 40 cm apart, as shown on the figure. An object is placed 60 cm in front of the first lens as show in second figure.
a) Find the position of the final image formed by the combination of the two lenses?
b) Find magnification of the final image formed by the combination of the two lenses?
 
Two lens system
L - Distance between two lenses
f1 - Focal length of first lens
f2 - Focal length of second lens
do1 - Distance to object
di1 - Distance to image created from first lens
do2 - Distance to object for second lens (which is the image create from first lens)
hi1 - First image height
hi2 -Second image height
m1 - magnification for first lens
m2 - magnification for second image

To determine the image distance, the lens equation can be used.
lens equation

Apply lens equation to first lens
lens equation
image distance
image distance
image distance
di1 = 12 cm First image located 12 cm behind the first lens

Image generated from first lens going to be object for the second lens

do2 = L – di1

do2 = 40 cm – 12 cm

do2 = 28 cm

Lets apply lens equation to second lens
lens equation
image distance for second lens
image distance

di2 = 32.31 cm

Final image located at 32.31 cm behind second lens.

Lens magnification can be find using
magnification
lens one magnification
m1 = - 0.2

First lens has magnification of – 0.2
Image magnification in terms of object and image height can be write
magnification using height
magnification
height ratio

First lens has magnification of – 0.2, the image is inverted and is 0.2 times of original height.

Lets apply image magnification equation to second lens
magnification for second lens
magnification
m2 = - 1.15

Second lens has magnification of – 1.15
Image magnification in terms of object/image height is
magnification using height
magnification

Image generated from first lens going to be object for the second lens

hi1 = ho2
magnification
Total magnification
Total magnification
Final height
Final height

From this equation we see that total magnification is the product of m1 and m2.

Total magnification is 0.23, is a positive number, final image is not inverted but it is smaller than original object.
 
[ Back ]