Question

If the ratio of amplitudes of two light waves is 2 : 1, then the ratio between the intensities of the two waves is

• A. $4 : 1$
• B. $1 : 1$
• C. $1 : 2$
• D. $1 : 4$
• E. $2 : 1$

Hint:

Intensity is proportional to the square of amplitude: $I \propto A^2$.

Answer 1

The Correct Option is A

Step 1: The intensity of a wave is proportional to the square of its amplitude: \[ I \propto A^2 \] 
Step 2: Given that the amplitude ratio is $2:1$, let $A_1 = 2A$ and $A_2 = A$. 
Step 3: The intensity ratio is: \[ I_1 : I_2 = (2A)^2 : (A)^2 \] \[ = 4A^2 : A^2 = 4 : 1 \] 
Step 4: Therefore, the correct answer is (A).