A thin lens is made from a material with refractive index of 1.20. This lens may be used in either air (n = 1.00) or water (n = 1.33). Which of the following is true?

A. if the lens is converging in air then it is diverging in water, and if it is diverging in air then it is converging in water.

B. if the lens is converging in air then it is converging in water, and if it is diverging in air then it is diverging in water.

C. if the lens is converging in air then it is diverging in water, but if it is diverging in air then it is still diverging in water.

D. if the lens is converging in air then it is still converging in water, but if it is diverging in air then it is converging in water.

E. it is impossible to know whether the lens will be converging or diverging in water just from knowing the refractive index of the lens and whether it is converging or diverging in air.

A) true. We see the equations and it would appear that the sign changes when you pass from one medium to the other

Explanation:

The expression for the focal length of a thin lens is

1 / f = (n'-n) ( / 1/R₁ - 1 / R₂)

In this equation n 'and n are the refractive indexes of the lens and the surrounding environment respectively

For converging lenses f is positive and for diverging lenses f is negative

Let's write this equation for both media

Air (n = 1)

1 / f₁ = (1.20-1) (1/R₁ - 1/R₂)

1 / f₁ = 0.2 (1/R₁ - 1/R₂)

Water (n = 1.33)

1 / f₂ = (1.20 - 1.33) (1/R₁ - 1/R₂)

1 / f₂ = - 0.13 (1/R₁ - 1/R₂)

We see that the sign of the focal length changes

Now we can analyze the claims

A) true. We see the equations and it would appear that the sign changes when you pass from one medium to the other

B) false. The focal length sign changes

C) False. The two signs change

D) False. The focal length sign changes

E) False. We cannot know the value, but change of characteristic