Question

A totally reflecting, small plane mirror placed horizontally faces a parallel beam of light, as shown in the figure. The mass of the mirror is 20 g. Assume that there is no absorption in the lens and that 30% of the light emitted by the source goes through the lens. Find the power of the source needed to support the weight of the mirror.

(Use h = 6.63 × 10^-34J-s = 4.14 × 10^-15 eV-s, c = 3 × 10⁸ m/s and me = 9.1 × 10^-31kg)

Answer 1

Given :-

Mass of the mirror, m = 20 g = 20 × 10⁻³ kg

The weight of the mirror will be balanced if the force exerted by the photons will be equal to the weight of the mirror.

Now,

Relation between wavelength `(λ)` and momentum (p) :-

`p = h/λ`

On divinding both sides by t , we get 

`P/t = h/(λt)...............(1)`

Energy,

`E = (hc)/λ`

⇒ `E/t = (hc)/(λt)`

Let P be the power. Then,

`P = E/t = (hc)/(λt)`

`P = (pc)/t ............ ["Using equation (1)"]`

⇒ `P/c = p/t`

Force , 

`F = P/t = P/c   ..............("Since F" = ("Momentum")/("Time"))`

Thus, rate of change of momentum = Power/c

As the light gets reflected normally,

Force exerted = 2 (Rate of change of momentum) = 2 × Power/c

`30% "of" ((2 xx "Power")/c) = "mg"`

`⇒ "Power" = (20 xx 10^-3 xx 10 xx 3 xx 10^8 xx 10)/(2 xx 3)= 100" MW"`