Question

In a biprism experiment, the distance between \(4^{th}\) and \(13^{th}\) bright band on the same side is '\(y\)' when light of wavelength \(6000\) Å is used. For a light of wavelength '\(λ\)' the distance between \(6^{th}\) and \(16^{th}\) bright band on the same side is again '\(y\)'. The value of '\(λ\)' in Å units is

• A. \(6500\)
• B. \(6300\)
• C. \(5400\)
• D. \(4800\)

Hint:

Fringe width is proportional to wavelength; count the number of fringe widths.

Answer 1

The Correct Option is C

Step 1: Fringe width relation:
$\beta\propto\lambda$, so the total distance $y = N\beta$ is proportional to $N\lambda$, with $N$ the number of fringe widths.

Step 2: Same y means same N times lambda:
$9\times6000 = 10\times\lambda$.

Step 3: Solve:
$\lambda = 5400$ $\text{\AA}$.

Final Answer:
lambda is 5400 angstrom, option (C). \[ \boxed{5400\ \text{\AA}} \]