A-level Physics (Advancing Physics)/Young's Slits/Worked Solutions

1. A 2-slit experiment is set up in which the slits are 0.03 m apart. A bright fringe is observed at an angle 10° from the normal. What sort of electromagnetic radiation was being used?

$\lambda =d\sin {\theta }=0.03\times \sin {10}\approx 5.21\times 10^{-3}{\mbox{ m}}$

So, microwaves were being used.

2. Light, with a wavelength of 500 nm, is shone through 2 slits, which are 0.05 m apart. What are the angles to the normal of the first three dark fringes?

$n\lambda =2d\sin {\theta }\,$

$n\times 500\times 10^{-9}=2\times 0.05\times \sin {\theta }$, where n is an odd integer.

$\theta =\arcsin {\frac {n\times 500\times 10^{-9}}{0.05\times 2}}=\arcsin {(n\times 500\times 10^{-8})}$

Then, substitute in n = 1,3 and 5 to gain corresponding values of θ:

n	θ (°)
1	2.9 x 10−4
3	8.6 x 10−4
5	1.4 x 10−3

3. Some X-rays, with wavelength 1 nm, are shone through a diffraction grating in which the slits are 50 μm apart. A screen is placed 1.5 m from the grating. How far are the first three light fringes from the point at which the normal intercepts the screen?

$n\times 10^{-9}={\frac {50\times 10^{-6}\times x}{1.5}}\approx 33.3\times 10^{-6}\times x$, where n is an integer.

$x={\frac {n\times 10^{-9}}{33.3\times 10^{-6}}}=30\times 10^{-6}\times n$

Then, substitute in n = 1,2 and 3 to gain corresponding values of x:

n	x (m)
1	30 x 10−6
2	60 x 10−6
3	90 x 10−6