Two thin lenses, when in contact, produce a combination of power +10 dioptre. When they are 0.25 m part, the power reduces to +6 diopter. The focal length of the lenses are

Q: Two thin lenses, when in contact, produce a combination of power +10 dioptre. When they are 0.25 m part, the power reduces to +6 diopter. The focal length of the lenses are ….m and … m

Sol: When the lenses in contact,

P = P₁ + P₂

or, P₁ + P₂ = 10 … (i)

When lenses have d separation,

P₁ + P₂ – d P₁ P₂ = P

or, P₁ + P₂– 0.25(P₁ P₂) = 6

or, 10 – 0.25(P₁ P₂) = 6

or, P₁ P₂ = 16 … (ii)

From (i) and (ii) , we get

P₁ = 8 D , P₂ = 2 D

∴  f₁ = 1/8 = 0.125 m , f₂ = 1/2 = 0.5 m