focal length immersed in water

Question

A convex lens has a focal length of 40 cm in air. What is the focal length when immersed in water? Index of refraction for air-glass is 1.54, ? for air-water is 1.33.

Answer 1

For a thin lens, the focal length depends on the refractive index difference between the lens and the surrounding medium:

1/f ∝ (n_lens / n_medium − 1)

In air:

n_lens = 1.54

n_air ≈ 1

So,

(n_lens / n_air − 1) = (1.54 / 1 − 1) = 0.54

Since f_air = 40 cm, we have:

1/f_air ∝ 0.54

In water:

n_water = 1.33

(n_lens / n_water − 1) = (1.54 / 1.33 − 1)

= 1.158 − 1

= 0.158

So,

1/f_water ∝ 0.158

Taking the ratio:

f_water / f_air = 0.54 / 0.158

= 3.42

Therefore,

f_water = 40 × 3.42

= 136.8 cm

Final Answer:

The focal length in water is approximately 137 cm (about 1.37 m).