Question

Two identical glass ng=1.6 equiconvex lenses of focal length f are kept in contact. the space between two lenses is filled with a liquid ni=1.4 . the focal length of the combination is :

Answer 1

The focal length of the combination is f/1.4

Given:

ng = 1.6

ni = 1.4

Focal length of convex lens = f

Explanation:

The focal length of convex lens is given by the formula:

1/f = (ng - 1) (2/R)

1/f = (1.6 - 1) (2/R)

1/f = 0.6 (2/R)

R/f = 1.2 ⇒ (equation 1)

The focal length of lens when filled with water is given by the formula:

1/f' = (ni - 1) (-2/R)

1/f' = (1.4 - 1) (-2/R)

1/f' = 0.4 (-2/R)

R/f' = -0.8 ⇒ (equation 2)

Now, the equivalent focal length is given by the formula:

1/feq = 1.2/f -0.8/f + 1/f

1/feq = (1.2 - 0.8 + 1)/f

1/feq = 1.4/f

∴ feq = f/1.4