Question

In a certain region of the screen, number of fringes formed is observed to be 8 in Young's double slit experiment when light of wavelength \(6600 \text{Å}\) is used. If the light of wavelength \(4400 \text{Å}\) is used, the number of fringes observed in the same region of the screen will be

• A. \(10\)
• B. \(12\)
• C. \(16\)
• D. \(18\)

Hint:

Fringe width is proportional to wavelength, so the number in a fixed region is inversely proportional to it.

Answer 1

The Correct Option is B

Step 1: Use fringe widths:
$\beta_2 = \beta_1\times\frac{4400}{6600} = \frac23\beta_1$.

Step 2: Count:
The region now holds $\frac{3}{2}$ times as many fringes: $8 \times \frac32 = 12$.

Final Answer:
The number of fringes is $12$, option (B). \[ \boxed{12} \]