# CIE AS & A Level Physics : 8.4 The diffraction grating – Exam style question – Paper 2

### Question

(a) For a progressive wave, state what is meant by wavelength.
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………… 
(b) A light wave from a laser has a wavelength of 460nm in a vacuum.
Calculate the period of the wave.

period = ……………………………………………… s 

(c) The light from the laser is incident normally on a diffraction grating.
Describe the diffraction of the light waves at the grating.
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………… 
(d) A diffraction grating is used with different wavelengths of visible light. The angle θ of the
fourth-order maximum from the zero-order (central) maximum is measured for each
wavelength. The variation with wavelength λ of sinθ is shown in Fig. 4.1. (i) The gradient of the graph is G.
Determine an expression, in terms of G, for the distance d between the centres of two

adjacent slits in the diffraction grating.

d = …………………………………………………
(ii) On Fig. 4.1, sketch a graph to show the results that would be obtained for the
second-order maxima.

Ans:

(a) distance moved by wavefront/energy during one cycle/oscillation/period (of source)
or
minimum distance between two wavefronts
or

(b) v =λ / T
or
v = fλ and f = 1 / T

$$T = 460 \times 10^{–9} / 3.00 \times 10^8$$

$$= 1.5\times 10^{–15} s$$

(c) waves pass through/enter the slit(s)
(d)(i) n λ = d sin θ
G = sin θ / λ
d = 4 / G

(d)(ii) straight line from 400 nm to 700 nm that is always below printed line
straight line has smaller gradient than printed line and is 5 small squares high at wavelength of 700 nm

### Question

(a) For a progressive wave, state what is meant by:
(i) the wavelength
………………………………………………………………………………………………………………………….
………………………………………………………………………………………………………………………….

(ii) the amplitude.
………………………………………………………………………………………………………………………….
………………………………………………………………………………………………………………………….

(b) A beam of red laser light is incident normally on a diffraction grating.

(i) Diffraction of the light waves occurs at each slit of the grating. The light waves emerging from the slits are coherent.
Explain what is meant by:
1. diffraction
……………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………
2. coherent.
……………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………

(ii) The wavelength of the laser light is 650nm. The angle between the third order diffraction maxima is 68°, as illustrated in Fig. 4.1. Calculate the separation d between the centres of adjacent slits of the grating.

d = …………………………………………….. m

(iii) The red laser light is replaced with blue laser light.
State and explain the change, if any, to the angle between the third order diffraction maxima.
………………………………………………………………………………………………………………………….
………………………………………………………………………………………………………………………….
………………………………………………………………………………………………………………………….

(a)(i)

distance moved by wavefront / energy during one cycle / vibration / oscillation / period (of source)
or
minimum distance between two wavefronts
or

(a)(ii)

maximum displacement (of particle / point on wave)

(b)(i)

1   light / waves spread (at each slit)

2   constant phase difference (between light / waves)

(b)(ii)

n λ = d sin θ

d = 3 × 650 × 10–9 / sin34°

d = 3.5 × 10–6 m

(b)(iii)

wavelength of blue light is shorter (than 650 nm / red light)

so angle (between third order diffraction maxima) decreases

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