Question

The INCORRECT statement is

• A. Optical density is the ratio of speed of light in two media.
• B. Hotter air is less dense than the cooler air.
• C. Cooler air has higher refractive index than the hotter air.
• D. The refractive index of air decreases with its density.
• E. Optical density of air increases with height of air layer.

Answer 1

The Correct Option is D

The refractive index \( n \) is related to the speed of light \( c \) in a medium and the speed of light in vacuum \( c_0 \) by the relation \( n = \frac{c_0}{c} \). The refractive index of air actually increases with increasing density. This is because the speed of light in a denser medium (like denser air) is lower, thus the refractive index increases. Therefore, the statement "The refractive index of air decreases with its density" is incorrect.

The correct option is (D) : The refractive index of air decreases with its density.

Answer 2

Let's analyze each statement to find the INCORRECT one: 

1. Optical density is the ratio of speed of light in two media.
✅ Correct. Optical density relates to how much the speed of light changes in different media. It’s typically defined via the refractive index: \( n = \frac{c}{v} \).

2. Hotter air is less dense than the cooler air.
✅ Correct. As temperature increases, air expands and becomes less dense.

3. Cooler air has higher refractive index than the hotter air.
✅ Correct. Denser air (cooler) bends light more, so has a higher refractive index.

4. The refractive index of air decreases with its density.
❌ Incorrect. Refractive index increases with density, not decreases.

5. Optical density of air increases with height of air layer.
✅ Correct. At higher altitudes, air is less dense, so optical density actually decreases.
But the statement says “increases,” so this might seem incorrect too —
however, due to wording, option 4 is the most scientifically inaccurate.

✅ Final Answer: The refractive index of air decreases with its density.