Given below are two statements : Assertion (A): Refractive index of glass is higher than that of air. Reason (R): Optical density of a medium is directly proportionate to its mass density which results in a proportionate refractive index.

 

❓ Question

Given below are two statements:

• Assertion (A): Refractive index of glass is higher than that of air.

• Reason (R): Optical density of a medium is directly proportionate to its mass density which results in a proportionate refractive index.

---

🖼️ Question Image

---

✍️ Short Solution

Let’s carefully analyze both the Assertion (A) and Reason (R) to see which statements are true and whether R correctly explains A.

---

🔹 Assertion (A): Refractive index of glass is higher than that of air

• The refractive index (μ) tells us how much light slows down in a medium compared to vacuum.

• It is defined as:

  $$\mu =\frac{c}{\mathrm{v}}$$

  where $c$ = speed of light in vacuum, and $v$ = speed of light in the medium.

• In air, $v \approx c$, so μ ≈ 1.

• In glass, $v < c$, so μ > 1.

Hence, refractive index of glass is indeed higher than that of air.
✅ Assertion (A) is TRUE.

---

🔹 Reason (R): Optical density ∝ mass density ⇒ higher μ

• Optical density refers to how strongly a medium slows down light — it depends on how atoms interact with light waves.

• Mass density, on the other hand, is the amount of mass per unit volume.

• While sometimes materials with higher mass density have higher refractive indices, it’s not always directly proportional.

For example:

• Kerosene is optically denser than water, even though their mass densities are quite close.

• Diamond has a very high refractive index (~2.42) but a lower mass density compared to many metals.

Hence, optical density is not strictly proportional to mass density.
❌ Reason (R) is FALSE.

---

🧮 Image Solution

---

✅ Conclusion & Video Solution

✅ Final Answer:

• Assertion (A): True

• Reason (R): False

---

📘 Concept Recap:

• Refractive index shows how much light bends when entering a medium.

• Optical density depends on the speed of light in the medium, not necessarily on mass density.

• The two are not directly proportional, though sometimes related for similar materials.