Question

In double slit experiment, the angular width of the fringes is \(0.20^{\circ }\) for sodium light (\(\lambda =5890\ \text{Å}\)). To increase the angular width of the fringes by \(10\%\), the necessary change in wavelength is

• A. zero
• B. increase by \(6479\ \text{Å}\)
• C. decrease by \(589\ \text{Å}\)
• D. increase by \(589\ \text{Å}\)

Hint:

Angular fringe width is directly proportional to the wavelength.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The angular width of fringes in a double slit experiment is \(\theta=\dfrac{\lambda}{d}\), so \(\theta\propto\lambda\) for a fixed slit separation.

Step 2: Apply the Change
To raise \(\theta\) by \(10\%\), the wavelength must also rise by \(10\%\).
\(\lambda'=1.1\times 5890=6479\ \text{Å}\)

Step 3: Calculation
Change in wavelength \(=6479-5890=589\ \text{Å}\) (an increase).

Step 4: Compare the options
This matches option (D).

Final Answer:
The wavelength must be increased by 589 angstrom. \[ \boxed{\text{(D) }\text{increase by }589\ \text{Å}} \]