Question

Light with an energy flux of 20 W/cm² falls on a non-reflecting surface at normal incidence. If the surface has an area of 30 cm² the total momentum delivered (for complete absorption) during 30 minutes is ______.

Options

• 36 × 10^–5 kg m/s

• 36 × 10^–4 kg m/s

• 108 × 10⁴ kg m/s

• 1.08 × 10⁷ kg m/s

Answer 1

Light with an energy flux of 20 W/cm² falls on a non-reflecting surface at normal incidence. If the surface has an area of 30 cm² the total momentum delivered (for complete absorption) during 30 minutes is `underline(36 xx 10^-4 kg m/s)`.

Explanation:

Given, energy flux `phi` = 20 W/cm²

Area, A = 30 cm²

Time, t = 30 min = 30 × 60 s

Now, total energy falling on the surface in time t is

U = `phi`AT = 20 × 30 × (30 × 60) J

Momentum of the incident light = `U/c`

= `(20 xx 30 xx (30 xx 60))/(3 xx 10^8)` = 36 × 10^–4 kg ms^–1

Momentum of the reflected light = 0

∴ Momentum delivered to the surface = 36 × 10^–4 – 0 = 36 × 10^–4 kg ms^–1

As no reflection from the surface and for complete absorption so the momentum of reflected radiation is zero.

Momentum delivered to surface = Change in momentum

= `p_f - p_t = 0 - 36 xx 10^-4 = - 36 xx 10^-4` kg m/s

(–) sign shows the direction of momentum.