You are given three lenses L1, L2, L3 each of focal . . .

Question : You are given three lenses L₁, L₂, L₃ each of focal length 20 cm. An object is kept at 40 cm in front of L₁. The final real image is formed at the focus I of L₃. Find the separation between L₁, L₂ and L₃.

Doubt by Eshani 

Solution : 

f₁=f₂=f₃=+20 cm

For Lens L₁
u₁=-40 cm

f₁=+20 cm

Using Thin Lens Formula

Now, 

v₁=u₁f₁/(u₁+f₁)

v₁=(-40)(20)/(-40+20)
v₁=-800/-20
v₁=40 cm 

For Lens L₃

v₃=+20 cm

f₃=+20 cm

Now, 

u₃=v₃f₃/(f₃-v₃)
u₃=(20)(20)/(20-20)
u₃=400/0
u₃=∞

For Lens L₂

v₂=+∞

f₂=+20 cm

1/f₂=1/v₂-1/u₂ 

1/20=1/∞-1/u₂
1/20=-1/u₂

u₂=-20 cm

Hence, distance between L1 and L2 is given by 

= |v₁|+|u₂|
= |40|+|-20|
= 40+20
= 60 cm

Distance between L₂ and L₃ is given by
=|v₂|+|u₃|

=|∞| + |∞|
= ∞

Hence, the distance between L₂ and L₃ could be any distance. The exact distance between the Lens L2 and L3 can't be calculated. 

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Similar Question :

You are given three lenses L₁, L₂ and L₃ each of focal length 10 cm. An Object is kept at 15 cm in front of L₁, as shown. The final real image is formed at the focus 'F' of L₃. Find the separations between L₁, L₂ and L₃.

Doubt by Sonali

Ans : 

Distance between L₁ and L₂ = 40 cm

Distance between L₂ and L₃ = ∞ [Can't be exactly calculated]