# 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#

Find the slit width, $$a_i$$, for pattern (i) (use the small angle approximation if it applies). Express your answer in $$\mu$$m to three significant figures. Take the distance you measured on Fig. (i) in Part 2 to be 1.00 cm, and the distance to the screen to be 60.0 cm.

Please enter in a numeric value in $$\mu$$m.

## Part 2#

Find the slit width, $$a\_{ii}$$, for pattern (ii) (use the small angle approximation if it applies). Express your answer in $$\mu$$m to three significant figures. Take the distance you measured on Fig. (ii) in Part 2 to be 2.30 cm, and the distance to the screen to be 60.0 cm.

Please enter in a numeric value in $$\mu$$m.

## Part 3#

Do your answers to part 1 and 2 make sense in terms of which pattern indicated has the larger slit width?

• Yes, because the wider patterm should come from the larger slit width.

• Yes, because the less wide pattern should come from the larger slit width.

• No, because the wider pattern should come from the larger slit width.

• No, because the less wide pattern should come from the larger slit width.

• There is no relation between slit width and width of the pattern.