Chapter 19, Problem 9STP

To determine

The wavelength of light.

Answer to Problem 9STP

  $5.7\times {10}^{-7}\text{m}$

Explanation of Solution

Given:

Number of slits per centimeter, $N=6000\text{slits/cm}$

Order, $n=1$

Diffraction angle, $\theta =20°$

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)

  $d=\frac{1}{N}$

Calculations:

The distance between slits can be calculated as follows:

  $\begin{array}{c}d=\frac{1}{N}\\ =\frac{1}{6000}\text{cm}\\ \text{=1}\text{.67}\times {\text{10}}^{-6}\text{m}\end{array}$

  $\begin{array}{c}d\sin \theta =n\lambda \\ \lambda =\frac{d\sin \theta }{n}\\ =\frac{1.67\times {10}^{-6}\times \sin 20°}{1}\\ =5.7\times {10}^{-7}\text{m}\end{array}$

Conclusion:

Thus, the wavelength of the light is $5.7\times {10}^{-7}\text{m}$ .