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

To find the force exerted by the beam of light on the surface, we first need to understand how the power of the light and its reflection relate to force. When light strikes a surface, it can either be absorbed or reflected. In this case, the surface absorbs 70% of the incident light and reflects the remaining 30%. Let's break this down step by step.

Understanding Power and Force

The power of the incident beam is given as 10 W. Since the surface absorbs 70% of this power, we can calculate the absorbed power:

• Absorbed Power = 70% of Incident Power
• Absorbed Power = 0.70 × 10 W = 7 W

The remaining power, which is reflected, can also be calculated:

• Reflected Power = 30% of Incident Power
• Reflected Power = 0.30 × 10 W = 3 W

Calculating the Force

To find the force exerted by the light on the surface, we can use the relationship between power, momentum, and force. The momentum carried by light can be expressed as:

• Momentum (p) = Power (P) / Speed of Light (c)

The speed of light (c) is approximately 3 × 10⁸ m/s. The change in momentum when light reflects off a surface is twice the momentum of the reflected light because it reverses direction. Therefore, the force (F) exerted on the surface can be calculated using the formula:

• Force (F) = Change in Momentum / Time

Since we are dealing with power, we can relate it directly to force as follows:

• F = 2 × (Reflected Power / c)

Now, substituting the values:

• F = 2 × (3 W / (3 × 10⁸ m/s))
• F = 2 × (3 / 3 × 10⁸)
• F = 2 × (1 × 10^-8)
• F = 2 × 10^-8 N

Final Result

The force exerted by the beam of light on the surface is therefore:

This calculation illustrates how even a small amount of power can exert a measurable force when considering the principles of momentum and reflection in light. If you have any further questions or need clarification on any part of this process, feel free to ask!