The pressure exerted by an electromagnetic wave of intensity l `("watt/m"^(2))` on a nonreflecting surface is [c is the velocity of light]

Options

A. lc
B. `lc^(2)`
C. `l//c`
D. `l//c^(2)`

Explanation

To solve the problem of finding the pressure exerted by an electromagnetic wave of intensity \( I \) on a non-reflecting surface, we can follow these steps:

### Step 1: Understand the Relationship Between Intensity and Energy
The intensity \( I \) of an electromagnetic wave is defined as the power per unit area. Mathematically, it can be expressed as:
\[ I = \frac{P}{A} \]
where \( P \) is the power and \( A \) is the area.

### Step 2: Relate Intensity to Momentum
The momentum \( p \) of a photon can be expressed in terms of its energy \( E \) as:
\[ p = \frac{E}{c} \]
where \( c \) is the speed of light. For an electromagnetic wave, the energy \( E \) can be related to intensity \( I \) over an area \( A \):
\[ E = I \cdot A \cdot t \]
where \( t \) is the time duration.

### Step 3: Calculate Momentum Per Unit Area
To find the momentum per unit area, we can substitute \( E \) into the momentum equation:
\[ \text{Momentum per unit area} = \frac{E}{cA} = \frac{I \cdot A \cdot t}{cA} = \frac{I \cdot t}{c} \]
Since we are interested in the pressure, we will consider the momentum change per unit time.

### Step 4: Consider the Non-Reflecting Surface
For a non-reflecting surface, the photons do not reflect back. Therefore, the change in momentum \( \Delta p \) when the wave strikes the surface is equal to the initial momentum:
\[ \Delta p = \frac{I \cdot t}{c} \]
The final momentum is zero since the photons are absorbed.

### Step 5: Relate Change in Momentum to Force
The force \( F \) exerted on the surface can be defined as the rate of change of momentum:
\[ F = \frac{\Delta p}{\Delta t} = \frac{I}{c} \]
where \( \Delta t \) is the time interval over which the momentum change occurs.

### Step 6: Define Pressure
Pressure \( P \) is defined as force per unit area:
\[ P = \frac{F}{A} \]
Substituting the expression for force:
\[ P = \frac{I}{c} \]

### Final Result
Thus, the pressure exerted by an electromagnetic wave of intensity \( I \) on a non-reflecting surface is given by:
\[ P = \frac{I}{c} \]