Question

In double slit experiment, the angular width of the fringes is 0.20° for the sodium light (λ = 5890 Å). In order to increase the angular width of the fringes by 10%, the necessary change in the wavelength is

• A. Increase of 589 Å
• B. Decrease of 589 Å
• C. Increase of 6479 Å
• D. Zero

Answer 1

Answer: (A)

Increase of 589 Å

Answer 2

By using $\theta = \frac{\lambda}{d}$

⇒ $\frac{\theta_{1}}{\theta_{2}} = \frac{\lambda_{1}}{\lambda_{2}}$

⇒ $\frac{0.20^{o}}{(0.20^{o} + 10\%\text{of}0.20)} = \frac{5890}{\lambda_{2}}$ ⇒ $\frac{0.20}{0.22} = \frac{5890}{\lambda_{2}}$

⇒ $\lambda_{2} = 6479$

So increase in wavelength = 6479 – 5890 = 589 Å.