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

< A-level Physics (Advancing Physics) < Young's Slits

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?

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

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

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

n	θ (°)
1	5.730 x 10^-4
3	5.2360 x 10^-7
5	8.7266 x 10^-7

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

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