Question 4
4
7 marks
Question 4(b)
4(b)
A laser produces a narrow beam of coherent light of wavelength 632 nm . The beam is incident normally on a diffraction grating, as shown in Fig. 4.1. Spots of light are observed on a screen placed parallel to the grating. The distance between the grating and the screen is 165 cm . The brightest spot is P . The spots formed closest to P and on each side of P are X and Y . X and Y are separated by a distance of 76 cm . Calculate the number of lines per metre on the grating. number per metre =
Mediumstructured4 marks
Answer
\(\tan \theta=\frac{38}{165}\) \(\theta=13^{\circ}\) ……………………………………………………………………. C1 number \(=(1 / d=) 3.6 \times 10^{5} \quad \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \quad\) A1 [4]
Question 4(c)
4(c)
The grating in (b) is now rotated about an axis parallel to the incident laser beam, as shown in Fig. 4.2. State what effect, if any, this rotation will have on the positions of the spots P, X and Y .
Mediumstructured2 marks
Answer
P remains in same position ………………………………………………… ㅡ1 X and Y rotate through \(90^{\circ}\) ……………………………………………………. B1 [2]
Question 4(d)
4(d)
In another experiment using the apparatus in (b), a student notices that the distances XP and PY , as shown in Fig. 4.1, are not equal. Suggest a reason for this difference.
Mediumstructured1 marks
Answer
either screen not parallel to grating or grating not normal to (incident) light B1
Question 5
5
6 marks
Question 5(b)
5(b)
A laser emits a beam of electromagnetic waves of frequency \(3.7 \times 10^{15} \mathrm{~Hz}\) in a vacuum.
structured6 marks
Question 5(b)(iii)
5(b)(iii)
The beam from the laser now passes through a diffraction grating with 2400 lines per millimetre. A detector sensitive to the waves emitted by the laser is moved through an arc of \(180^{\circ}\) in order to detect the maxima produced by the waves passing through the grating, as shown in Fig. 5.2. Calculate the number of maxima detected as the detector moves through \(180^{\circ}\) along the line shown in Fig. 5.2. Show your working.
Hardstructured4 marks
Answer
\(d \sin \theta=n \lambda\) or \((1 / N) \times \sin \theta=n \lambda\) C1 \[ \begin{aligned} d & =1 / 2400 \times 10^{3}(\mathrm{~m}) & =4.2 \times 10^{-7}(\mathrm{~m}) \end{aligned} \] or \[ N=2400 \times 10^{3}\left(\mathrm{~m}^{-1}\right) \] C1 \[ \begin{aligned} n=4.2 \times 10^{-7} \times \sin 90^{\circ} / 8.1 \times 10^{-8} \text { or } \sin 90^{\circ} / 2400 \times 10^{3} \times 8.1 \times 10^{-8} n=5.2 \text { or } 5.1 \text { or } \text { when } n=5, \theta=76.4^{\circ} \text { and when } n=6, \sin \theta>1 \text { (so) } n=5 \end{aligned} \] B1 number of maxima \(=(2 \times 5)+1\) \[ \text { = } 11 \] A1
Question 5(b)(iv)
5(b)(iv)
The laser is now replaced with one that emits electromagnetic waves with a wavelength of 300 nm . Explain, without calculation, what happens to the number of maxima now detected. Assume that the detector is also sensitive to this wavelength of electromagnetic waves.
Mediumstructured2 marks
Answer
the wavelength has increased M1 (so) number of maxima decreases A1
Question 25
25
Which electromagnetic wave phenomenon is needed to explain the spectrum produced when white light falls on a diffraction grating?
Easymcq1 marks
Answer
B
Question 4
4
6 marks
Question 4(a)
4(a)
Describe the diffraction of monochromatic light as it passes through a diffraction grating.
Mediumstructured2 marks
Answer
waves pass through the elements / gaps / slits in the grating M1 spread into geometric shadow A1
Question 4(b)
4(b)
White light is incident on a diffraction grating, as shown in Fig. 4.1. The diffraction pattern formed on the screen has white light, called zero order, and coloured spectra in other orders.
structured4 marks
Question 4(b)(ii)
4(b)(ii)
Light of wavelength 625 nm produces a second-order maximum at an angle of \(61.0^{\circ}\) For to the incident direction. Determine the number of lines per metre of the diffraction grating.
Mediumstructured2 marks
Answer
\(n \lambda=d \sin \theta\) C1 \(N=\sin 61^{\circ} /\left(2 \times 625 \times 10^{-9}\right)=7.0 \times 10^{5} \quad\) A1
Question 4(b)(iii)
4(b)(iii)
Calculate the wavelength of another part of the visible spectrum that gives a maximum for a different order at the same angle as in (ii). wavelength = nm
Mediumstructured2 marks
Answer
\(n \lambda=2 \times 625\) is a constant (1250) C1 \(n=1 \rightarrow \lambda=1250\) outside visible \(n=3 \rightarrow \lambda=417 \mathrm{in}\) visible \(n=4 \rightarrow \lambda=312.5\) outside visible \(\lambda=420 \mathrm{~nm}\) A1 [2]
Question 26
26
A diffraction grating with 500 lines per mm is used to observe diffraction of monochromatic light of wavelength 600 nm . The light is passed through a narrow slit and the grating is placed so that its lines are parallel to the slit. Light passes through the slit and then the grating. An observer views the slit through the grating at different angles, moving his head from X parallel to the grating, through Y , opposite the slit, to Z parallel to the grating on the opposite side. How many images of the slit does he see? 3 4 6 7
Mediummcq1 marks
Answer
D
Question 26
26
A diffraction grating with N lines per metre is used to diffract light of various wavelengths \(\lambda\). The graph shows the relation between the diffraction angle \(\theta\) and \(\lambda\) for different wavelengths in the \(n^{\text {th }}\) order interference pattern. What is the gradient of the graph? N n \(\frac{N}{n}\) \(\frac{n}{N}\) \(\frac{1}{N n}\)
Hardmcq1 marks
Answer
A
Question 26
26
Light of frequency \(6.7 \times 10^{14} \mathrm{~Hz}\) in a vacuum is incident normally on a diffraction grating that contains \(4.0 \times 10^{5}\) lines \(\mathrm{m}^{-1}\). What is the angle between the adjacent second and third order intensity maxima? \(12^{\circ}\) \(21^{\circ}\) \(33^{\circ}\) \(54^{\circ}\)
Hardmcq1 marks
Answer
A
Question 26
26
Light passes through a diffraction grating ruled at 1000 lines per cm and the same wavelength of light also passes through two narrow slits 0.5 mm apart. Both situations produce intensity maxima and minima on a screen. Which statement about the separation of the maxima on the screen and the sharpness of the maxima is correct? The diffraction grating maxima are less widely spaced and are less sharp than the two-slit maxima. The diffraction grating maxima are less widely spaced and are sharper than the two-slit maxima. The diffraction grating maxima are more widely spaced and are less sharp than the two-slit maxima. The diffraction grating maxima are more widely spaced and are sharper than the two-slit maxima.
Mediummcq1 marks
Answer
D
Question 26
26
A parallel beam of white light passes through a diffraction grating. Orange light of wavelength 600 nm in the fourth order diffraction maximum coincides with blue light in the fifth order diffraction maximum. What is the wavelength of the blue light? 450 nm 480 nm 500 nm 750 nm
Mediummcq1 marks
Answer
B
Question 27
27
A diffraction grating experiment is set up using yellow light of wavelength 600 nm . The grating has a slit separation of \(2.00 \mu \mathrm{~m}\). What is the angular separation ( \(\theta_{2}-\theta_{1}\) ) between the first and second order maxima of the yellow light? \(17.5^{\circ}\) \(19.4^{\circ}\) \(36.9^{\circ}\) \(54.3^{\circ}\)
Mediummcq1 marks
Answer
B