# Triple Slit Experiment#

A triple-slit experiment has a slit spacing $$d = 20 \rm{\mu m}$$ and is illuminated by a laser of wavelength $$\lambda = 500 \rm{nm}$$ and is a distance $$L = 10 \rm{cm}$$ from a screen.

## Part 1#

Without using the small angle approximation calculate the spacing between the $$m = 0$$ and $$m = {{ params.m }}$$ peaks.

Please enter in a numeric value in $$\rm{mm}$$.

## Part 2#

Without using the small angle approximation calculate the spacing between the $$m = 9$$ and $$m = 10$$ peaks.

Please enter in a numeric value in $$\rm{mm}$$.

## Part 3#

In the small angle approximation $$\tan(\theta) = \sin(\theta) = \theta$$, where $$\theta$$ is in radians. What is the spacing between the $$m = 0$$ and $$m = {{ params.m }}$$ peaks in the small angle approximation?

Please enter in a numeric value in $$\rm{mm}$$.

## Part 4#

What is the spacing between the $$m = 9$$ and $$m = 10$$ peaks in the small angle approximation?

Please enter in a numeric value in $$\rm{mm}$$.

## Part 5#

Based on your results in Parts 1-4 is the small angle approximation a good approximation for the spacing between the $$m = 0$$ and $$m = {{ params.m }}$$ peaks and the $$m = 9$$ and $$m = 10$$ peaks?

• It is a good approximation to the spacing between the $$m = 0$$ and $$m =$$ 1 peak, but not a great approximation to the spacing between the $$m = 9$$ and $$m = 10$$ peak as the angle for $$y_{10}$$ is just outside the range of validity of the small angle approximation.

• It is a good approximation to both spacings since the angles remain small out to $$m = 10$$.

• It is a not a good approximation either angle as one cannot meaningfully use the small angle approximation in diffraction problems even when the wavelength is small relative to the slit spacing.

## Part 6#

If the colour of the laser changed to purple with a wavelength $$\lambda = 400 \rm{nm}$$, how would the spacing change?