AQA AS Physics

Topic Questions

3.4 Diffraction

1a4 marks

The diffraction grating equation is given by: 

                     d sin θ = 

State the definition of the following variables and an appropriate unit for each. 

            (i)         d 

            (ii)        θ           

            (iii)       n 

            (iv)       λ

1b2 marks

A diffraction grating has 720 × 103 lines per m. 

Calculate the distance between adjacent slits of the grating.

1c3 marks

A narrow laser beam of wavelength 635 nm is directed normally onto the diffraction grating from part (b), as shown in Figure 1.

Figure 1

3-4-s-q--q1c-easy-aqa-a-level-physics

The first order diffracted beam makes an angle θ with the centre. 

Calculate the value of θ.

1d1 mark

With this laser beam, the highest order observed on the screen is the second. 

State how many minima are seen on the screen.

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2a2 marks

Diffraction gratings are used in spectrometers to split a beam of light into its consistent wavelengths. 

State two applications of a spectrometer.

2b2 marks

Figure 1 shows an example of a spectrometer where the angles of the diffracted beams can be measured.

Figure 1

3-4-s-q--q2b-easy-aqa-a-level-physics

When light is directly normally onto the spectrometer, it emerges from both A and B. 

State what is observed at: 

            (i)         Point A 

            (ii)        Point B

2c4 marks

As the telescope is rotated from the straight–through position, each of the four colours in Table 1 is observed as a bright line at its corresponding first–order diffraction angle. 

Table 1

Colour

Observed Order

orange

 

violet

 

green

 

blue

 

Number the colours in Table 1 in order observed as the telescope is rotated from the straight–through position from the centre, with 1 being the 1st colour observed and so on.

2d1 mark

State the maximum value of θ for which the observer will be able to view any light emerging from the grating.

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3a2 marks

Define the term diffraction.

3b2 marks

State one property of a wave that changes when it is diffracted and one that remains the same.

3c2 marks

Complete the sentence by using an answer from the box. 

_____________ passing through  _____________ will produce a large diffraction effect.

3-4-s-q--q3c-easy-aqa-a-level-physics

3d4 marks

Figure 1a shows a laser emitting green light directed at a single slit, where the slit width is greater than the wavelength of the light.

Figure 1a

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The pattern on the screen may be represented as a graph of intensity against distance along the screen as shown in Figure 1b.

 Figure 1b

3-4-s-q--q3d-image-2-easy-aqa-a-level-physics

Complete Figure 1b by drawing the expected diffraction pattern on the screen.

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4a2 marks

In a laboratory experiment, monochromatic light from a laser of wavelength λ is incident normal to a diffraction grating. 

The diffracted waves are received on a white screen which is parallel to the plane of the grating. Figure 1 shows the position of the diffraction maxima. 

Figure 1

3-4-s-q--q4a-easy-aqa-a-level-physics

Sketch on Figure 1 angles theta subscript 2 and theta subscript 5, the angular separation between the second and fifth order of maxima respectively.

4b3 marks

The spacing between each slit in the grating is 2.45 µm. 

Calculate the number of lines per metre for this grating.

4c3 marks

The third–order spectral line is formed at an angle of 36º from the normal to the grating. 

Calculate the value of λ.

4d1 mark

State the order that would produce the brightest image on the white screen.

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5a3 marks

Wavefronts of a water wave pass through a gap in a harbour, as shown in Figure 1. 

Figure 1

3-4-s-q--q5a-easy-aqa-a-level-physics

Sketch the wavefronts on Figure 1 after they have passed through the gap.

5b4 marks

An X–ray beam of wavelength λ is diffracted by thin crystals that act like a diffraction grating. 

The wavefronts from the grating pass through the gaps of width d between the crystals to produce two orders of maxima on a photographic plate. These wavefronts are at angle θ to the normal, as shown in Figure 2.

 Figure 2

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Draw a line from each variable to the corresponding value of x that it represents in the diagrams in the right column.

3-4-s-q--q5b-image2-easy-aqa-a-level-physics

5c1 mark

State the ratio lambda over d in terms of angle θ for the first order diffraction.

5d2 marks

Two physicists Lucy and Amber are in disagreement over the highest order observed on the photographic plate. The highest order n is calculated from the ratio d over lambda. 

Lucy calculates this value to be 3.6 and says the highest order must therefore be 3. Amber disagrees and says the value should be rounded up to 4. 

State who is correct and explain your answer.

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1a4 marks

Figure 1 shows a section of a diffraction grating. Monochromatic light of wavelength lambda 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

3-4-s-q--q1a-hard-aqa-a-level-physics

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

            2 lambdad sin θ

1b3 marks

The adjacent lines on the diffraction pattern are 4lambda apart. 

Calculate the angle between the third order and second order maxima.

1c3 marks

The diffraction grating is placed 3.2 m from a screen. 

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

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2a3 marks

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.

2b3 marks

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. 

At what order of diffracted light will the two wavelengths be most distinguishable?

2c2 marks

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

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

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3a6 marks

In a laboratory experiment, monochromatic light of wavelength 550 nm from a laser is incident normal to a diffraction grating. The diffracted waves are received on a white screen which is parallel to the plane of the grating and 2.5 m from it. Figure 1 shows the positions of the diffraction maxima with distances measured from the central maximum. 

Figure 1

3-4-s-q--q3a-hard-aqa-a-level-physics

By means of a graphical method, use the measurements in Figure 1 to determine a mean value for the number of slits per metre on the grating.

3b3 marks

Describe and explain the effect, if any, on the appearance of the diffraction pattern when: 

            (i) Using a grating which has less slits per unit length.

            (ii) Using a laser source which has a wavelength of 650 nm.

            (iii) Decreasing the distance between the grating and the screen.           

3c4 marks

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

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Figure 2b

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

3d2 marks

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.

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4a2 marks

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

3-4-s-q--q4a-hard-aqa-a-level-physics

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

3-4-s-q--q4a-image-1-hard-aqa-a-level-physics

4b3 marks

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.

4c2 marks

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

3-4-s-q--q4c-hard-aqa-a-level-physics

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.

4d4 marks

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 position11.2 cm from the slit.

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5a3 marks

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

3-4-s-q--q5a-hard-aqa-a-level-physics

Show that the maximum wavelength of light for the centre of three orders to be seen on the screen is around 610 nm.

5b3 marks

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

3-4-s-q--q5b-hard-aqa-a-level-physics

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.

5c3 marks

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

3-4-s-q--q5c-hard-aqa-a-level-physics

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 alpha.

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

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1a3 marks

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.

1b3 marks

Calculate the highest order which is observable.

1c3 marks

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

1d2 marks

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.

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2a3 marks

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

Figure 1

3-4-s-q--q2a-medium-aqa-a-level-physics

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.

2b3 marks

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

2c3 marks

 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.

2d2 marks

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

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3a2 marks

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

Describe the pattern observed on the screen.

3b2 marks

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

3-4-s-q--q3b-medium-aqa-a-level-physics

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

3c3 marks

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. 

3d3 marks

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

Figure 2

3-4-s-q--q3d--medium-aqa-a-level-physics

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

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4a4 marks

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.

4b3 marks

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

4c2 marks

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

Calculate the angle for the third order maximum.

4d2 marks

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.

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5a4 marks

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

 

First order

Second order

Third order

red

25.2°

58.4°

not possible

blue

17.5°

37.0°

64.4°

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

5b3 marks

The red light has a wavelength of 720 nm.

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

5c2 marks

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.

5d3 marks

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.

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