Question

1. If you have the focal length of the first and second lenses f1 = 150 mm and f2 = 75 mm respectively, object distance from the first lens d0 = 280 mm and distance between lenses d = 440 mm, calculate the image distance after the second lens and image magnification of the two-lens system. In order to calculate magnification, use the object height value of 10 mm

f₁ = 150 mm

f₂ = 75 mm

Object distance from the first lens d₀ = 280 mm

Distance between lenses d = 440 mm

Image distance_____________

Magnification______________

2. Now keep all the parameters the same except for the object distance which is d0 = 200 mm now. Again, calculate the image distance after the second lens and image magnification of the two-lens system

Answer 1

1)

using lens equation for first lens :

1/f1 = 1/di + 1/do

1/150 = 1/di + 1/280

di = 323.07 mm

Now d o for second lens = 440 - 323.07

= 116.93 mm

using lens equation for second lens

1/f2 = +1/di + 1/do

1/75 = 1/di + 1/116.93

di = 209.15 mm

Therefore image distance = 209.15 mm to the right of second lens or 649.15 mm to the right of first lens

Magnification = m1*m2

= 323.07*209.15/(280*116.93)

= 2.06

2)

using lens equation for first lens :

1/f1 = 1/di + 1/do

1/150 = 1/di + 1/200

di = 600 mm

Now d o for second lens = 440 - 600

= -160 mm

using lens equation for second lens

1/f2 = +1/di + 1/do

1/75 = 1/di + 1/(-160)

di = 51.06 mm

Therefore image distance = 51.06 mm to the left of second lens

Magnification = m1*m2

= -600*51.06/(200*160)

= - 0.96