Question

In young's double slit experiment, the ratio of intensities of bright and dark bands is $16$ which means:

• A. The ratio of their amplitude is$5$.
• B. Intensities of individual sources are $25$ and$9$ units respectively.
• C. The ratio of their amplitudes is $4$.
• D. Intensities of individual sources are $4$ and $3$ units respectively.

Answer 1

The correct option is B

Intensities of individual sources are $25$ and$9$ units respectively.

Solution:

Step 1: Given information

The ratio of intensities of bright and dark bands$=$$16$.

$\Rightarrow \frac{I_{max}}{I_{min}}=16$

Step 2: Calculate the ratio of amplitude

Let$I_1$ and$I_2$ represent the intensities of individual sources with amplitudes $A_1$ and$A_2$, respectively.

Bright fringe intensity $=I_{max}=(\surd I_1+I_2{)}^2$…..(i)

Dark fringe intensity $=I_{min}={(\surd I_1–I_2)}^2$…..(ii)

From (i) and (ii),

$\Rightarrow$$\frac{I_{max}}{I_{min}}=16$ ….. (From given)

By solving (i) and (ii),

$\Rightarrow$ $\frac{\surd I_1}{\surd I_2}=\frac{5}{3}$

$I_2=9units\Rightarrow I_1=25units$

Furthermore, the amplitude is proportional to the intensity.

Therefore, the Ratio of amplitude$=\frac{A_1}{A_2}=\frac{\surd I_1}{\surd I_2}=\frac{5}{3}$.

Hence, the correct option is (B).