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:

'''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: