# Diffraction#

Photographs of the diffraction of a red laser of wavelength $$\lambda = 650$$ nm are shown in figures (i) and (ii). A line of length $$7$$ cm indicates the length scale on the screen.

## Useful Info#

When monochromatic light of wavelength $$\lambda$$ passes through a double slit of separation $$d$$, constructive interference occurs at angles $$\theta_m$$, where $$d\sin\theta_m = m\lambda$$ and $$m = {0, 1, 2, ...}$$ is an integer. This same relation holds true for light passing through a diffraction grating. Light passing through a single slit will destructively interfere at angles $$a\sin\theta_p = p \lambda$$, where $$p = {1, 2, 3, ..}$$ is a non-zero integer and $$a$$ is the slit width. If a screen is placed at a distance $$L$$ behind the slit(s)/grating, bright and dark lines are observed at a distance $$y$$ from the central maximum given by $$y = L\tan\theta$$. When the small angle approximation $$\theta \approx \sin\theta \approx \tan\theta$$ is valid ($$\theta \ll 1$$ expressed in radians), one expects a double-slit pattern to display equally spaced bright maxima, whereas a single-slit pattern exhibits a central maximum that is twice as wide as the subsequent maxima.

## Part 1#

If the screen was 60 cm away from the diffraction that caused these patterns, to how many digits after the decimal would the small angle approximation ($$\theta \approx$$ tan$$^{-1} \theta$$) hold for the largest angle?