Ncert Exercises & Solutions

An EM wave of intensity \(I\) falls on a surface kept in a vacuum and exerts radiation pressure \(P\) on it. Which of the following are true?

(a)	Radiation pressure is \(\frac{I}{c}\) if the wave is totally absorbed.
(b)	Radiation pressure is \(\frac{I}{c}\) if the wave is totally reflected.
(c)	Radiation pressure is \(\frac{2I}{c}\) if the wave is totally reflected.
(d)	Radiation pressure is in the range \(\frac{I}{c}<P<\frac{2I}{c}\) for real surfaces.

1. (a, b, c)
2. (b, c, d)
3. (a, c, d)
4. (c, d)

(a, c, d) Hint: The radiation pressure depends on the energy transferred to the surface.

Step 1: Find the radiation pressure.
Radiation pressure (p) is the force exerted by an electromagnetic wave on the unit area of the surface, i.e., rate of change of momentum per unit area of the surface.

Momentum per unit time per unit area

= \frac{Intensity}{Speed of wave} = \frac{I}{c}

Change in momentum per unit time per unit area =

\frac{∆ I}{c}

= radiation pressure (p)

i.e.,

p = \frac{∆ I}{c}

The momentum of the incident wave per unit time per unit area =

\frac{I}{c}

Step 2: Find the radiation pressure for the absorbed wave.

When the wave is fully absorbed by the surface, the momentum of the reflected wave per unit time per unit area = 0.

Radiation pressure (p) = change in momentum per unit time per unit area =

\frac{∆ I}{c} = \frac{I}{c} - 0 = \frac{I}{c}

Step 3: Find the radiation pressure for the reflected wave.

When the wave is totally reflected, then the momentum of the reflected wave per unit time per unit

area = - \frac{I}{c}, Radiation pressure p = \frac{I}{c} - (- \frac{I}{c}) = \frac{2 I}{c}

Hence, p lies between \frac{I}{c} and \frac{2 I}{c} for a real surface as the wave is partially reflected

by a real surface .

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