Question

two concave lenses each of focal length 20cm and refractive index 3/2 are kept in contact with each other. if the space between two lenses is filled with water of refractive index mue =4/3.the magnitude of the focal length of combination is
1)15 cm
2)20cm
3)25cm
4)30cm

Answer 1

n effect we have a combination of 3 lens , the liquid between the two double convex lens forming a double concave lens.

We need to find the focal length of this liquid lens, through it has the same radius of curvature R.

For double convex lens,

1f=(μ−1)[1R+1R]1f=(μ−1)[1R+1R]

∴1f=(32−1)[1R+1R]∴1f=(32−1)[1R+1R]

∴f=R∴f=R

For the liquid lens :

1f′=(μ2−1)[−1R−1R]1f′=(μ2−1)[−1R−1R]

=13(−2R)=13(−2R)

1f′=−23f1f′=−23f

Now the focal length of combination

1F=1f+1f+1f1F=1f+1f+1f

=2f−23f=2f−23f

=43f=43f

∴F=3f4∴F=3f4

Hence d is the correct answer.