CBSE 2025, Set 2

Question

A laser beam of wavelength $500	ext{ nm}$ and power $5	ext{ mW}$ strikes normally on a perfectly reflecting surface of area $1	ext{ mm}^2$ of a body. It rebounds back from the surface. Find the force exerted by the laser beam on the body.

Edvaya · Accepted Answer

The correct answer is Subjective. Given:
* Wavelength $\lambda = 500	ext{ nm} = 500 	imes 10^{-9}	ext{ m}$
* Power $P = 5	ext{ mW} = 5 	imes 10^{-3}	ext{ W}$
* Area $A = 1	ext{ mm}^2$ (not required for force calculation)

The energy of a single photon is $E = \frac{hc}{\lambda}$.
The number of photons striking the surface per second is $n = \frac{P}{E} = \frac{P}{(hc/\lambda)}$.

The momentum of a single photon is $p = \frac{h}{\lambda}$.
Since the surface is perfectly reflecting, the photon rebounds with the same momentum magnitude but opposite direction. 
The change in momentum per photon is $\Delta p = p - (-p) = 2p = \frac{2h}{\lambda}$.

The total force $F$ exerted by the beam is the total change in momentum per second:
$$F = n 	imes \Delta p$$
$$F = \left( \frac{P}{hc/\lambda} ight) 	imes \left( \frac{2h}{\lambda} ight)$$
$$F = \frac{2P}{c}$$

Substitute the given values:
$$F = \frac{2 	imes 5 	imes 10^{-3}}{3 	imes 10^8}$$
$$F = \frac{10 	imes 10^{-3}}{3 	imes 10^8}$$
$$F = 3.33 	imes 10^{-11}	ext{ N}$$

$$\boxed{F = 3.33 	imes 10^{-11}	ext{ N}}$$

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Physics > Modern Physics > Dual Nature Of Radiation And Matter

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