A beam of white light is incident normally on a plane surface absorbing 70% of the light and reflecting the rest.If the incident beam carries 10 W of power,find the force exerted by it on the surface.

To determine the force exerted by the beam of white light on the surface, we need to consider how much power is reflected and how that relates to the force. When light strikes a surface, it can either be absorbed or reflected. In this case, 70% of the light is absorbed, and 30% is reflected. Let's break this down step by step.

Understanding Power Reflection

The total power of the incident beam is given as 10 W. Since 70% is absorbed, we can calculate the power that is reflected:

• Power absorbed = 70% of 10 W = 0.70 × 10 W = 7 W
• Power reflected = 30% of 10 W = 0.30 × 10 W = 3 W

Calculating the Force

The force exerted by the light on the surface can be derived from the change in momentum of the light as it reflects off the surface. When light reflects, it changes direction, which means it experiences a change in momentum. The momentum of light is given by the equation:

Momentum (p) = Energy (E) / Speed of Light (c)

For light, the energy is related to power and time. The force (F) can be expressed in terms of the rate of change of momentum:

Force (F) = Change in momentum per unit time

Since the light reflects off the surface, the change in momentum for the reflected light can be calculated as:

Change in momentum = 2 × (Power reflected / c)

Here, we multiply by 2 because the momentum changes direction upon reflection. The speed of light (c) is approximately 3 × 10⁸ m/s.

Putting It All Together

Now, substituting the values into the formula:

• Power reflected = 3 W
• c = 3 × 10⁸ m/s

Now we can calculate the force:

F = 2 × (Power reflected / c) = 2 × (3 W / (3 × 10⁸ m/s))

Calculating this gives:

F = 2 × (3 / (3 × 10⁸)) = 2 × (1 × 10^-8) = 2 × 10^-8 N

Final Result

The force exerted by the beam of light on the surface is approximately 2 × 10^-8 N. This small force illustrates how even a seemingly insignificant amount of light can exert pressure when it interacts with a surface, thanks to the principles of momentum and energy transfer.