The Diffraction Grating (CIE AS Physics)

A teacher explains a diffraction investigation to a group of physics students.

'In this investigation a laser will be used to shine monochromatic light of wavelength 581.9 nm onto a diffraction grating. The light passing through the grating will therefore be coherent.'

Define the following terms used by the teacher

During the investigation, a second-order maximum is produced at an angle of 35° measured from the normal to the grating.

Calculate the angular separation between the highest order and second order maxima.

The investigation is repeated using the same grating but a different monochromatic source.

In this experiment, the second-order maximum is observed at an angle of 25.7°.

Calculate the wavelength of this second source.

A laser produces a monochromatic light of wavelength 581.9 nm which falls normally on a diffraction grating. A second order maximum is produced at an angle of 35° measured from the normal to the grating.

Calculate the number of lines per metre on the grating.

Calculate the highest order which is observable.

Calculate the angular separation between the highest order and second order maxima.

When the same grating is used with a different monochromatic source, the second-order maximum is observed at an angle of 25.7°. 

Calculate the wavelength of this second source.

A helium-neon laser produces monochromatic light of wavelength 672 nm which falls perpendicular on a diffraction grating which has 350 lines per mm. 

Calculate the angle between the second-order maxima.

Show that the highest order image shown in this arrangement is n = 4.

A different laser that produces monochromatic light of wavelength  falls perpendicular to a diffraction grating from which adjacent lines are 5 apart. 

Calculate the angle for the third order maximum.

The diffraction grating is placed 2.7 m from a screen. 

Hence or otherwise, calculate the distance between the third diffraction order and the normal to the grating as measured on the screen.

Students in a laboratory have created the following set-up shown in Fig 1.1. Parallel rays of monochromatic light from two adjacent slits A and B of wavelength $\lambda$ are incident normally on a diffraction grating with a slit separation $\mathrm{d.}$

Fig. 1.1

Use the diagram to derive the equation nλ = dsinθ where θ  is the angle of diffraction of a maxima order n visible on a screen.

The monochromatic light in the set-up in part (a) has a wavelength of 499 nm. The graph in Fig. 1.2 shows the variation of sinθ with the order n of the maximum. The central order corresponds to n = 0.

Fig. 1.2

Determine a mean value for the number of slits per mm of the grating.

The grating is 30 mm wide.

Determine the number of slits required to obtain a maximum of five bright fringes on the screen.

The students claim that they observed the following diffraction pattern in Fig. 1.3 on the screen for the grating from part (c).

Fig. 1.3

State two reasons why the interference pattern obtained cannot be correct. 

A narrow beam of coherent light of wavelength 520 nm is incident upon a diffraction grating that has 3.10 × 10² lines per mm. The diffraction pattern is seen on a screen. 

Calculate the maximum number of minima that could be seen on the screen.

A different light source is incident upon the same diffraction grating. A student suspects there are two wavelengths of light in this incident beam, one of wavelength 490 nm and another of wavelength 490.2 nm. 

Determine the highest order of the visible diffracted light. 

The minimum angular separation for which the two wavelengths may be differentiated is 0.05^­­º. 

Deduce whether the student observed the two wavelengths as distinct images at this order. Support your answer with calculations ignoring the blurring effect often observed at higher order maxima.            

Fig. 1.1 shows the shortest wavelength of this light incident on the screen after the other has been removed from part c). 

Fig. 1.1

Determine the distance between the diffraction grating and the screen, D.