Question

A radiation of energy \(\mathrm{E}\) falls normally on a Perfect reflecting surface. The momentum transferred to the surface is. (A) \((\mathrm{E} / \mathrm{c})\) (B) \((2 \mathrm{E} / \mathrm{c})\) (C) \(\left(\mathrm{E} / \mathrm{c}^{2}\right)\) (D) Ec

Short answer

The momentum transferred to the reflecting surface is (B) \((2 \mathrm{E} / \mathrm{c})\).

Step-by-step solution

Understand the concept of reflection and conservation of momentum.

During reflection, the direction of the momentum changes, but the magnitude remains the same. As the surface is perfectly reflecting, the momentum before and after reflection will be the same in magnitude but opposite in direction. Therefore, the total momentum transferred to the reflecting surface will be twice the initial momentum.

Calculate the initial momentum of the radiation.

Using the given relationship E = pc, we can find the initial momentum of the radiation. To find the value, we need to rearrange the equation as p = E/c.

Calculate the momentum transferred to the surface.

As mentioned earlier, since the surface is perfectly reflecting, all the initial momentum of the radiation is transferred to the surface. Therefore, the momentum transferred to the surface is 2*(initial momentum). From step 2, we found the initial momentum to be E/c, so the momentum transferred to the surface will be 2*(E/c) = 2E/c. The correct answer is (B) \((2 \mathrm{E} / \mathrm{c})\).