Physics 9702 · AS & A Level · The diffraction grating

The diffraction grating — practice question

(a) Sunlight arrives as parallel rays, striking a magnifying glass at normal incidence. The magnifying glass focuses the light onto region $A$ of radius $r$, as illustrated in Fig. 5.1. In cross-section, the magnifying glass is circular with radius $5.5\,\text{cm}$. The sunlight intensity incident on the magnifying glass is $1.3\,\text{kW m}^{-2}$. Assume that every ray incident on the magnifying glass passes through it.
(a(i))[2]

Calculate the power of the sunlight incident on the magnifying glass.

(a(ii))[1]

The radius is $1.5\,\text{mm}$. Determine the intensity of the light on area $A$.

(b(i))[2]

Show that the waves have wavelength $8.1 \times 10^{-8}\,\text{m}$.

(b(ii))[1]

State the region of the electromagnetic spectrum to which these waves belong.

(b(iii))[4]

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 $180^\circ$ to locate 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.

(b(iv))[2]

The laser is now replaced with one that emits electromagnetic waves with a wavelength of $300\,\text{nm}$. 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.

(c)[4]

Calculate the number of maxima detected as the detector moves through $180^{\circ}$ along the line shown in Fig. 5.2. Show your working.

(d)[2]

The laser is now replaced with one that emits electromagnetic waves with a wavelength of $300\,\text{nm}$. Explain, without calculation, how the number of maxima detected changes. Assume that the detector is also sensitive to electromagnetic waves of this wavelength.

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