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

From Wikibooks, open books for an open world
Jump to: navigation, search

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