Question

42.Three lenses are in contact have a combined focal length of 12cm.when the third lens is removed the combined focal length is 60/7 cm The third lens is -----------

Answer 1

The third lens is diverging with focal length -30 cm

Explanation :

We know that when lenses are combined, the combined focal length is given by the relation:

1/f = 1/f₁ + 1/f₂ + 1/f₃..........

so for 3 lenses,

1/f = 1/f₁ + 1/f₂ + 1/f₃

=> 1/12 = 1/f₁ + 1/f₂ + 1/f₃

But given the two lenses have combined focal length of 60/7, so

1/f₁ + 1/f₂ = 7/60

=> 1/12 = 7/60 + 1/f₃

=> 1/f₃ = 1/12 - 7/60 = -2/60

=> f₃ = -30 cm

Hence the third lens is diverging with focal length -30 cm