A convex and a concave lens separated by distance d are then put in contact. The focal length of the combination

Step-by-step solution

Let f₁ and f₂ are focal lengths of convex and concave lens respectively, when they are kept in contact co-axially, then focal length F of the combination is given as aligned 1 F &= 1 f₁ + 1 (-f₂ ) [ array l Focal length of concave lens is negative. array ] 1 F &= f₂-f₁ f₁ f₂ F &= f₁ f₂ f₂-f₁ aligned When both lenses are kept at a distance d , then their combined focal length F^ is given as aligned 1 F^ &= 1 f₁ + 1 (-f₂ ) - d f₁ (-f₂ ) 1 F^ &= 1 f₁ - 1 f₂ + d f₁ f₂ 1 F^ &= f₂-f₁+d f₁ f₂ F^ &= f₁ f₂ f₂-f₁+d aligned F