Chapter 19, Problem 5STP

To determine

To Choose: The correct option.

Answer to Problem 5STP

Option B

Explanation of Solution

Given:

Distance between slits, $d=0.055\text{mm}$

Order, $n=1$

Wavelength of light, $\lambda =650\text{nm}\text{=}\text{650}\times {\text{10}}^{-9}\text{m}$

Formula used:

The condition for bright fringes to form:

  $\begin{array}{l}d\sin \theta =n\lambda \\ \left(n=0,\pm 1,\pm 2,\pm \mathrm{3.....}\right)\end{array}$

(path difference = whole number of wavelengths)

Calculations:

Substitute the values:

  $\begin{array}{c}\theta ={\sin }^{-1}\left(\frac{n\lambda }{d}\right)\\ ={\sin }^{-1}\left(\frac{1\times 650\times {10}^{-9}}{0.055\times {10}^{-3}}\right)\\ =0.68°\end{array}$

Conclusion:

Thus, option B is correct.