Question

When two light waves, both with wavelength \(\lambda\) and amplitude \(A\), interfere constructively, they produce a light wave of the same wavelength but with amplitude \(2 A\). What is the intensity of this light wave? a) same intensity as the original waves b) double the intensity of the original waves c) quadruple the intensity of the original waves d) Not enough information is given.

Short answer

Question: When two light waves with the same wavelength and amplitude interfere constructively, the intensity of the resulting light wave is __________ the intensity of the original waves. a) the same as b) half c) quadruple d) double Answer: c) quadruple

Step-by-step solution

Find the amplitude of the resulting wave

Since the two light waves interfere constructively, they will produce a light wave of the same wavelength with amplitude \(2A\).

Calculate the intensity of the original waves

If we denote the intensity of the original waves as \(I_0\), we can say that \(I_0\) is proportional to the square of the amplitude of the original waves (\(A^2\)): \(I_0 \propto A^2\)

Calculate the intensity of the resulting wave

We need to find the intensity of the resulting light wave, \(I\). Since \(I\) is proportional to the square of the amplitude of the resulting wave ((\(2A)^2\)), we have: \(I \propto (2A)^2 = 4A^2\)

Compare the intensities

Since we can see that the intensity of the resulting wave is four times the intensity of the original waves (\(I = 4I_0\)), we can conclude that the intensity of the resulting light wave is quadruple the intensity of the original waves. The correct answer is c) quadruple the intensity of the original waves.