A plane electromagnetic wave of wave intensity 6 Wm^-2 strikes a small mirror of area 30 cm^2,

step 1 We are given that a plane electromagnetic wave has intensity i equal to 6 watt per meter square

A plane electromagnetic wave of wave intensity 6 Wm^-2...

A plane electromagnetic wave of wave intensity $6 \mathrm{Wm}^{-2}$ strikes a small mirror of area $30 \mathrm{~cm}^{2}$, held perpendicular to the approaching wave. The momentum transferred in $\mathrm{kg} \mathrm{ms}^{-1}$ by the wave to the mirror each second will be fa) 1. $2 \times 10^{-10}$ (b) $2.4 \times 10^{-4}$ (c) $3.6 \times 10^{-11}$ (d) $4.8 \times 10^{-7}$

A plane electromagnetic wave of wave intensity $6 \mathrm{Wm}^{-2}$ strikes a small mirror of area $30 \mathrm{~cm}^{2}$, held perpendicular to the approaching wave. The momentum transferred in $\mathrm{kg} \mathrm{ms}^{-1}$ by the wave to the mirror each second will be
fa) 1. $2 \times 10^{-10}$
(b) $2.4 \times 10^{-4}$
(c) $3.6 \times 10^{-11}$
(d) $4.8 \times 10^{-7}$

Key Concepts

Area of the Reflective Surface

The area of the surface that intercepts the electromagnetic wave determines the total power received from the wave. Proper conversion of units (e.g., converting from cm² to m²) is essential in ensuring the accurate calculation of both the force due to radiation pressure and the resulting momentum transfer.

Momentum Transfer in Reflection

When light reflects off a surface, such as a mirror, it undergoes a change in momentum, which results in a force on the surface. The momentum change is doubled compared to absorption because the light reverses its direction upon reflection. This principle is used to calculate the momentum transferred per second (impulse) to the mirror.

Electromagnetic Wave Intensity

This concept refers to the power transmitted per unit area by an electromagnetic wave. It is a measure of how much energy is delivered by the wave per unit time over a certain area and is crucial in determining how much energy or momentum is available to interact with objects such as mirrors.

Radiation Pressure

Radiation pressure is the pressure exerted by electromagnetic radiation on a surface. For a perfectly reflecting surface, the radiation pressure is related to the intensity of the incident wave by the formula P = 2I/c, where I is the intensity and c is the speed of light. This concept is essential when calculating the force exerted by light on the mirror.

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