Angle q can never be greater than 90° for a diffraction grating. If a question asks you to find the maximum number of images, let q = 90° and find the value for n. Since sin 90° = 1, the formula will
become nλ = d(1) or n = d
__ λ .
(Remember that n must be an integer.)
r1 S1 d S2 a θ (r2 θ – r1 ) l b
FIG. 18.4 Taking a magnified view of the light passing through a grating enables us to find a formula for the wavelength of light
H r2 screen S1 d θ S2 r2 – r1 r2 = d sin θ r1
The pattern from a diffraction grating leads to a method for calculating the wavelength of light. If we take a magnified view of the light passing through a grating, we can break this down to find a formula for the wavelength (Fig. 18.4).
This formula can be used to calculate wavelength or grating distance:
Wavelength of light nλ = d sin θ
n = order of image, λ = wavelength (m), d = grating constant (m), θ = angle of diffracted light from normal (°)
Derivation of nλ = d sin p Each slit gives a point source of light a distance d apart. The screen is a distance l from the slits.
Wherever a bright fringe occurs, the difference in distance from that point on the screen to each slit is an integer multiple of wavelengths. From Fig. 18.4a, this distance is r2 – r1. So: r2 – r1 = nλ
Since the distance for l is relatively very large compared to d, we can use trigonometric ratios: sin θ = opposite
______________ hypotenuse =
_______ d
r2 – r1
This can be seen in close up in Fig. 18.4b. So: d sin θ = r2 – r1.
