If a thin lens with an index of 1.5 has a dioptric power of +4.00 in air, what is its power if placed in water?

The power of a lens is influenced by the refractive indices of the lens material and the surrounding medium. In this case, the thin lens has a dioptric power of +4.00 diopters in air, which means that its focal length is 0.25 meters (since power in diopters is the inverse of the focal length in meters).

When a lens is placed in a different medium, such as water, the effective power of the lens changes because the refractive index of the new medium affects the lens’ ability to bend light.

To determine the new power in water, one must use the formula for lens power, which takes into account the refractive indices of both the lens and the surrounding medium. The formula is:

[ P_{medium} = P_{air} \times \left(\frac{n_{lens} - n_{medium}}{n_{lens} - n_{air}}\right) ]

Here:

• ( P_{air} ) is the original power (in air),

• ( n_{lens} ) is the refractive index of the lens (1.5),

• ( n_{medium} ) is the refractive index of water (approximately 1.33