Diffraction (AQA A Level Physics)

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 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 narrow beam of monochromatic light of wavelength 490 nm is directed normally at a diffraction grating, as shown in Figure 1. 

Figure 1

The number of lines per metre of the diffraction grating is 4.35 × 10⁵. 

Calculate the order of diffraction that is produced at an angle of 28° from the normal to the grating.

Calculate the number of positions of maximum intensity that are produced when the laser light is incident on the grating. Show your reasoning clearly.

 A different monochromatic light of wavelength 630.8 nm is incident upon the same diffraction grating and a screen is placed 4.5 m from the grating. 

Calculate the distance between the second diffraction order and the normal to the grating as measured on the screen.

Compare the appearance of the maxima between the two different monochromatic light sources.

White light is passed through a single narrow slit and illuminates a screen. 

Describe the pattern observed on the screen.

Blue light from a laser is now passed through a single narrow slit, as shown in Figure 1. A pattern of bright and dark regions can be observed on the screen which is placed several metres beyond the slit. 

Figure 1

Describe the effect on the diffraction pattern if the width of the narrow slit is decreased.

With the original slit width, state and explain the effect on the width of the fringes on the diffraction pattern if the blue light is replaced with a red light of the same intensity. 

The intensity graph for the diffracted blue light is shown in Figure 2. 

Figure 2

On the axes shown in Figure 2, sketch the intensity graph for the laser emitting red light.

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

Calculate the angle between the second order images.

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. 

Calculate the distance between the third diffraction order and the normal to the grating as measured on the screen.

A white-light source illuminates a diffraction grating that has 5.90 × 10⁵ lines per m. The light is incident normally on the grating. 

Table 1 shows the diffracting angles measured from the normal for the visible spectral orders using the grating. The angles are given for the red and blue ends of each spectrum. 

Table 1

 Use the value for the first order diffracting angle to calculate the wavelength of the blue light.

The red light has a wavelength of 720 nm.

Show that the third order maxima is not visible for the red light.

A monochromatic laser with blue light of the same wavelength as the blue light in the white-light source is now incident upon the same diffraction grating. The diffraction pattern is seen on a screen. 

Calculate the highest order maxima seen on the screen.

A student wants to accurately measure the wavelength of different monochromatic laser lights. They can choose between a diffraction grating arrangement or a two-slit interference arrangement. 

State which arrangement would allow the student to measure the wavelength of the different laser lights more accurately and give two reasons why.

Figure 1 shows a section of a diffraction grating. Monochromatic light of wavelength  is incident normally on its surface. Light waves are diffracted through angle θ from the second order image after passing through a converging lens (not shown). A, B and C are adjacent slits on the grating.

Figure 1

By considering the path between C and E, show that for a second order image 

            2 = d sin θ

A narrow beam of coherent light of wavelength 460 nm is incident upon a diffraction grating that has 2.80 × 10² lines per mm. The diffraction pattern is seen on a screen. 

Calculate the total number of minima 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 570 nm and another of wavelength 570.4 nm. 

Determine the order of diffracted light where the two wavelengths are most distinguishable.

The minimum angular separation for which the two wavelengths may be differentiated is 0.12^­­º. 

Deduce whether the student observed the two wavelengths as distinct images at this order. Support your answer with calculations.            

A scanning photometer is a device in which the voltage across an LDR (light dependent resistor) varies with the light intensity incident on the LDR. 

Figure 2a shows a laser beam of wavelength 623 nm normally incident on a diffraction grating. The LDR of a scanning photometer is moved across the diffracted beam and produces the scan shown in Figure 2b. This shows the central bright fringe with one further maximum (the first order image) on each side of it. The distance from the diffraction grating to the LDR is 265 mm.

Figure 2a

Figure 2b

Calculate the number of lines per mm on the diffraction grating.

The laser is changed to a different wavelength of light upon the same diffraction grating, which means the first order fringes are now 1.5 times further apart from each other than before. 

Calculate the wavelength of this new laser light.

In an investigation, a single loudspeaker is positioned behind a wall with a narrow gap as shown in Figure 1. 

A microphone attached to an oscilloscope enables changes in the amplitude of the sound to be determined for different positions of the microphone.

Figure 1a

The amplitude of sound is recorded as the microphone position is moved along the line AB a large distance from the gap. 

Draw on the graph in Figure 1b the results from the oscilloscope signal. 

Figure 1b

The signal generator is adjusted so that sound waves of the same amplitude but of a lower frequency are emitted by the loudspeaker. The investigation using the apparatus shown in Figure 1a is then repeated. 

Explain the effect this has on the graph drawn in part (a). Assume that the speed of the sound waves stay constant.

The set-up is now replaced so that laser light travels through a narrow slit to a screen, as shown in Figure 2.

Figure 2

Monochromatic light from the laser passes through the narrow slit to produce a diffraction pattern on the screen. The wavelength of the laser light is unknown.

Suggest one advantage and one disadvantage of obtaining the wavelength by using observations of a higher-order diffracted image.

The single slit is initially illuminated by light from a point source that is 3.50 cm from the slit. 

State and explain quantitatively how the intensity of the light incident on the single slit changes when the light source is moved to a position 11.2 cm from the slit.

A student sets up a monochromatic laser light such that it is incident along the normal to a diffraction grating of 400 lines per mm. The interference pattern is shown on a screen that is 30 cm long, and the distance between the grating and the screen is 14 cm, as shown in Figure 1. 

Figure 1

Show that the maximum wavelength of light for the centres of only three maxima to be seen on the screen is around 610 nm.

The screen is replaced with a metre rule as shown in Figure 2 and the laser light is replaced with one of a different wavelength. The axis of the rule is normal to the lines of the grating.

Figure 2

Bright lines are observed on the rule at the 20 cm, 25 cm, 15 cm, 31 cm and 9 cm marks. 

Calculate the angle between the first and second orders of diffraction.

The laser is replaced with a beam of white light which passes through a narrow slit and a different diffraction grating as shown in Figure 3. The ruler is replaced with a screen (not shown). The white light carries wavelengths which range from 420 nm to 690 nm.

Figure 3

It is found that the first-order spectrum shown on the screen is displaced from the straight-through position by an angle of 23º and the angular separation width of this spectrum is .

Calculate the angular separation, , of this first-order spectrum.