Chapter 19.1, Problem 15SSC

To determine

The angle up to which $\sin \theta \approx \tan \theta$ is a good approximation when the data has two significant figures.

Explanation of Solution

Introduction:

When light passes through a slit of the size comparable to the wavelength of the light, it diffracts. The light from one slit and the light from the second slit produce an interference pattern which is a repetition of bright and dark regions.

The equation for wave length from a double slit experiment is $d\sin \theta =m\lambda$ . It uses a simplification that as $\theta$ is small $\sin \theta \approx \tan \theta$ . This approximation for two significant digits is valid up to $9.9°$ . If the precision of the angle instrument is increased this approximation angle reduces to $2.99°$ .