Question

Interference fringes are obtained due to the interference of waves from two coherent sources of light with amplitudes ${a_1}$ and ${ a_2}$ (${a_1 =2a_2}$ ). What is the ratio of the maximum and minimum intensities of light in the interference pattern?
A) 2
B) 4
C) 9
D) ∞

Answer 1

According to the question we have to understand amplitudes are a and 2a hence we have to write their intensities in the ratio. From that we calculate by applying square root for both, from that we get maximum intensity and minimum intensity. By adding and subtracting respectively we get the final answer.

Complete answer:
Given amplitudes are a and 2a.
hence there intensities are in the ratio
\eqalign{ & {a^2}:{\left( {2a} \right)^2} \cr & \Rightarrow 1:4 \cr & \cr}
Hence we are getting the ratios of intensities i.e 1:4
So, consider the intensities are I and 4I
For finding maximum intensity we have to apply
maximum intensity= ${\left( {\sqrt I + \sqrt {4I} } \right)^2}$
$\therefore 9I$ is the maximum intensity.
Similarly for the minimum intensity we have
Minimum intensity = ${\left( {\sqrt I - \sqrt {4I} } \right)^2}$
Since the minimum intensity is I.

Hence the correct given option is C.

Additional information:
$\bullet$ Sometimes they ask conclusions like questions where we have to know the interference pattern can be produced by any two coherent waves moving in the same direction. And it cannot be concluded from the interference phenomenon that light is a transverse wave, as sound waves that are longitudinal in nature also interfere.
$\bullet$ We have to add some knowledge here that the speed of light in any medium depends on the refractive index of that medium, which is an intensive property. Therefore speed of light is not affected by the elasticity and inertia of the medium.

Note:
To solve these types of questions we have to know about Interference fringes, there we have clear ideas about the using light. Don`t forget to check related questions on this topic, put some extra effort into remembering those formulas where we are using accordingly.