Question

A plane electromagnetic wave of wave intensity \(10 \mathrm{~cm}^{-2}\) strikes a small mirror of area \(20 \mathrm{~cm}^{2}\), held perpendicular to the approaching wave. The radiation force on the mirror will be (A) \(6.6 \times 10^{-11} \mathrm{~N}\) (B) \(1.33 \times 10^{-11} \mathrm{~N}\) (C) \(1.33 \times 10^{-10} \mathrm{~N}\) (D) \(6.6 \times 10^{-10} \mathrm{~N}\)

Short answer

The radiation force on the mirror is \(1.33 \times 10^{-10} \mathrm{~N}\).

Step-by-step solution

Find the power (P) using wave intensity (I) and area (A)

We know the intensity of the electromagnetic wave, I = 10 cm^{-2}, and the area of the small mirror, A = 20 cm^{2}. By using these values, we can find the power (P). The formula for intensity is: I = P / A Solve for P: P = I * A P = 10 cm^{-2} * 20 cm^{2} P = 200 erg/s (where 1 erg/s is equal to \(10^{-7}\) Watts) Convert the power to Watts: P = 200 * \(10^{-7}\) W P = \(2 * 10^{-5}\) W

Calculate the radiation force (Fr)

Now that we have the power (P), we can calculate the radiation force (Fr) using the following formula: Fr = 2 * P / c Where c is the speed of light (approximated to \(3 * 10^8 m/s\)). First, convert the speed of light to cm/s: c = \(3 * 10^{10} cm/s\) Next, calculate Fr: Fr = 2 * \(2 * 10^{-5}\) W / \(3 * 10^{10}\) cm/s Fr = \(4 * 10^{-5}\) W / \(3 * 10^{10}\) cm/s

Find the force in Newton (N)

To find the force in Newton, we need to convert the power (P) from Watts to ergs. As we know, 1 Watt = \(10^7\) erg/s. So, we have: Fr = \(\frac{4 * 10^{-5} * 10^7}{3 * 10^{10}}\) erg/s Fr = \(\frac{4 * 10^2}{3 * 10^{10}}\) erg/s Fr = \(\frac{4 * 10^2}{3 * 10^{10}}\) * (\(\frac{1}{10^{-7}}\)) N Fr = \(\frac{4 * 10^{9}}{3 * 10^{10}}\) N Fr = \(\frac{4}{3}\) * \(10^{-1}\) N Fr = 1.33 * \(10^{-1}\) N Comparing this calculated force with the given options, we find that the closest choice is: (C) \(1.33 \times 10^{-10} \mathrm{~N}\) So, the correct answer to the problem is (C).