Question

An object is placed in a medium of refractive index 3. An electromagnetic wave of intensity $6 \times 10^8 \, \text{W/m}^2$ falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space = $3 \times 10^8$ m/s) :

• A. $36 \, \text{Nm}^{-2}$
• B. $18 \, \text{Nm}^{-2}$
• C. $6 \, \text{Nm}^{-2}$
• D. $2 \, \text{Nm}^{-2}$

Answer 1

Answer: (C)

$6 \, \text{Nm}^{-2}$

Answer 2

The radiation pressure $P$ is given by:

$P = \frac{I \cdot \mu}{c},$

where:
- $I$ is the intensity of the radiation,
- $\mu$ is the absorption coefficient (fraction of radiation absorbed, here $\mu = 1$ for total absorption),
- $c$ is the speed of light in a vacuum.

Substitute the given values:
- $I = 6 \times 10^8 \, \text{W/m}^2$,
- $\mu = 3$,
- $c = 3 \times 10^8 \, \text{m/s}$.

Calculate $P$:

$P = \frac{I \cdot \mu}{c} = \frac{6 \times 10^8 \cdot 3}{3 \times 10^8}.$

Simplify:

$P = 6 \, \text{N/m}^2.$

The Correct answer is: $6 \, \text{Nm}^{-2}$