DP Physics Questionbank

A student has four converging lenses of focal length 5, 20, 150 and 500 mm. Determine the maximum magnification that can be obtained with a refracting telescope using two of the lenses.

The incident ray shown in the diagram makes a significant angle with the optical axis.

(i) State the aberration produced by these kind of rays.

(ii) Outline how this aberration is overcome.

State the property of protons used in nuclear magnetic resonance (NMR) imaging.

Show that the attenuation coefficient for bone of density 1800 kg m^–3, for X-rays of 20 keV, is about 7 cm^–1.

Determine the distance between the lamp and the lens.

There are optical telescopes which have diameters about 10 m. There are radio telescopes with single dishes of diameters at least 10 times greater.

(i) Discuss why, for the same number of incident photons per unit area, radio telescopes need to be much larger than optical telescopes.

(ii) Outline how is it possible for radio telescopes to achieve diameters of the order of a thousand kilometres.

State the main physical difference between step-index and graded-index fibres.

The diagram shows a schematic view of a compound microscope with the focal points f_o of the objective lens and the focal points f_e of the eyepiece lens marked on the axis.

On the diagram, identify with an X, a suitable position for the image formed by the objective of the compound microscope.

The density of muscle is 1200 kg m^–3. Calculate the ratio of intensities to compare, for a beam of 20 keV, the attenuation produced by 1 cm of bone and 1 cm of muscle.

Calculate the focal length of the lens.

The angular diameter of the Moon at the naked eye is 7.8 × 10^–3 rad.

Calculate the angular diameter of the final image of the Moon.

On the diagram draw rays to locate the focal point of L₂. Label this point F.

The distance between the lenses is 18 cm. Determine the focal length of L₂.

Explain why, for the final image to form at infinity, the distance between the lenses must be 87.5 cm.

By reference to chromatic aberration, explain one advantage of a reflecting telescope over a refracting telescope.

State what is meant by a virtual image.

Show that the image of the object formed by L₁ is 12 cm to the right of L₁.

State two advantages of optic fibres over coaxial cables for these transmissions.

Suggest why infrared radiation rather than visible light is used in these transmissions.

A signal with an input power of 15 mW is transmitted along an optic fibre which has an attenuation per unit length of 0.30 dB$$km^–1. The power at the receiver is 2.4 mW.

Calculate the length of the fibre.

State and explain why it is an advantage for the core of an optic fibre to be extremely thin.

Describe how an ultrasound transducer produces ultrasound.

Calculate the acoustic impedance Z of muscle.

the radio-frequency signal emitted towards the patient.

The diagram shows a ray of light in air that enters the core of an optic fibre.

The ray makes an angle A with the normal at the air–core boundary. The refractive index of the core is 1.52 and that of the cladding is 1.48.

Determine the largest angle A for which the light ray will stay within the core of the fibre.

Identify the features of the output signal that indicate the presence of attenuation and dispersion.

The length of the optic fibre is 5.1 km. The input power of the signal is 320 mW. The output power is 77 mW. Calculate the attenuation per unit length of the fibre in dB$$km^–1.

Outline why the fracture in a broken bone can be seen in a medical X-ray image.

the non-uniform magnetic field applied to the patient.

On the diagram, sketch the part of wavefront X that is inside the lens.

On the diagram, sketch the wavefront in air that passes through point P. Label this wavefront Y.

Explain your sketch in (a)(i).

Determine the focal length of each lens.

The telescope is used to form an image of the Moon. The angle subtended by the image of the Moon at the eyepiece is 0.16 rad. The distance to the Moon is 3.8 x 10⁸ m. Estimate the diameter of the Moon.

State two advantages of the use of satellite-borne telescopes compared to Earth-based telescopes.

the large uniform magnetic field applied to the patient.

Ultrasound of intensity 0.012 W$$cm^–2 is incident on a water–muscle boundary. The acoustic impedance of water is 1.50 x 10⁶ kg$$m^–2$$s^–1.

The fraction of the incident intensity that is reflected is given by

$\frac{{\left(Z_2-Z_1\right)}^2}{{\left(Z_2+Z_1\right)}^2}$

where Z₁ and Z₂ are the acoustic impedances of medium 1 and medium 2.

Calculate the intensity of the reflected signal.

Two parallel rays are incident on a system consisting of a diverging lens of focal length 4.0 cm and a converging lens of focal length 12 cm.

The rays emerge parallel from the converging lens. Determine the distance between the two lenses.

In nuclear magnetic resonance (NMR) imaging radio frequency electromagnetic radiation is detected by the imaging sensors. Discuss the origin of this radiation.

The diagram shows X-rays incident on tissue and bone.

The thicknesses of bone and tissue are both 0.054 m.

The intensity of X-rays transmitted through bone is I_b and the intensity transmitted through tissue is I_t.

The following data are available.

Mass absorption coefficient for bone = mass absorption
coefficient for tissue = 1.2 × 10^–2$$m²$$kg^–1
Density of bone = 1.9 × 103 kg$$m^–3
Density of tissue = 1.1 × 103 kg$$m^–3

Calculate the ratio $\frac{I_{\text{b}}}{I_{\text{t}}}$.

State a typical frequency used in medical ultrasound imaging.

The screen is removed and the image is used as the object for a second diverging lens B, to form a final image. Lens B has a focal length of $2.00 \mathrm{cm}$ and the final real image is $8.00 \mathrm{cm}$ from the lens. Calculate the distance between lens A and lens B.

Calculate the total magnification of the object by the lens combination.

Lens A has a focal length of $4.00 \mathrm{cm}$. An object is placed $4.50 \mathrm{cm}$ to the left of A. Show by calculation that a screen should be placed about $0.4 \mathrm{m}$ from A to display a focused image.

Draw on the diagram the three wavefronts after they have passed through the lens.

Outline the meaning of normal adjustment for a compound microscope.

Explain the cause of the radio-frequency emissions from a patient’s body during nuclear magnetic resonance (NMR) imaging.

Outline how a gradient field allows NMR to be used in medical resonance imaging.

Calculate the maximum angle β for light to travel through the fibre.

Refractive index of core       = 1.50
Refractive index of cladding = 1.48

A technician operates an X-ray machine that takes 100 images each day. Estimate the width of the lead screen that is required so that the total exposure of the technician in 250 working days is equal to the exposure that the technician would receive from one X-ray exposure without the lead screen.

Determine the position of the image.

Explain, with appropriate calculations, why a gel is used between the transducer and the skin.

Outline how ultrasound is generated for medical imaging.

Describe one advantage and one disadvantage of using high frequencies ultrasound over low frequencies ultra sound for medical imaging.

Calculate the density of skin.

Suggest one reason why doctors use ultrasound rather than X-rays to monitor the development of a fetus. 

It is proposed to build an array of radio telescopes such that the maximum distance between them is 3800 km. The array will operate at a wavelength of 2.1 cm.

Comment on whether it is possible to build an optical telescope operating at 580 nm that is to have the same resolution as the array.

Calculate the maximum attenuation allowed for the signal.

Outline the formation of a B scan in medical ultrasound imaging.

State what is meant by half-value thickness in X-ray imaging.

A monochromatic X-ray beam of energy 20 keV and intensity I₀ penetrates 5.00 cm of fat and then 4.00 cm of muscle.

Calculate, in terms of I₀, the final beam intensity that emerges from the muscle.

Compare the use of high and low energy X-rays for medical imaging.

The diagram shows an incomplete ray diagram which consists of a red ray of light and a blue ray of light which are incident on a converging glass lens. In this glass lens the refractive index for blue light is greater than the refractive index for red light.

Using the diagram, outline the phenomenon of chromatic aberration.

Identify, with the letter X, the position of the focus of the primary mirror.

An optic fibre of refractive index 1.4475 is surrounded by air. The critical angle for the core – air boundary interface is 44°. Suggest, with a calculation, why the use of cladding with refractive index 1.4444 improves the performance of the optic fibre.

An amplifier can increase the power of the signal by 12 dB. Determine the minimum number of amplifiers required.

The graph shows the variation with wavelength of the refractive index of the glass from which the optic fibre is made.

Two light rays enter the fibre at the same instant along the axes. Ray A has a wavelength of λ_A and ray B has a wavelength of λ_B. Discuss the effect that the difference in wavelength has on the rays as they pass along the fibre.

In many places clad optic fibres are replacing copper cables. State one example of how fibre optic technology has impacted society.

determine the focal length of the lens.

calculate the linear magnification.

This arrangement using the secondary mirror is said to increase the focal length of the primary mirror. State why this is an advantage.

Distinguish between this mounting and the Newtonian mounting.

Identify whether the image is real or virtual.

The lens is 18 cm from the screen and the image is 0.40 times smaller than the object. Calculate the power of the lens, in cm^–1. 

Light passing through this lens is subject to chromatic aberration. Discuss the effect that chromatic aberration has on the image formed on the screen.

A system consisting of a converging lens of focal length F₁ (lens 1) and a diverging lens (lens 2) are used to obtain the image of an object as shown on the scaled diagram. The focal length of lens 1 (F₁) is 30 cm.

Determine, using the ray diagram, the focal length of the diverging lens.

Calculate the critical angle at the core−cladding boundary.

The use of optical fibres has led to a revolution in communications across the globe. Outline two advantages of optical fibres over electrical conductors for the purpose of data transfer.

Draw on the axes an output signal to illustrate the effect of waveguide dispersion.

Calculate the power of the output signal after the signal has travelled a distance of 3.40 km in the fibre.

Explain how the use of a graded-index fibre will improve the performance of this fibre optic system.

Hence state how the defect of the converging lens in (a) may be corrected.

Show that the longest path is 66 m longer than the shortest path.

Suggest how the refracted rays in (a) are modified when the converging lens is replaced by a diverging lens.

Calculate n.

Calculate the distance between the lenses.

Determine the time delay between the arrival of signals created by the extra distance in (b)(i).

Determine the magnification of the microscope.

Describe how the measurement in (b) provides diagnostic information for the doctor.

Determine, in terms of I₀, the intensity of ultrasound that is reflected at the muscle–bone boundary.

Ultrasound of intensity 50 mW m^-2 is incident on a muscle. The reflected intensity is 10 mW m^-2. Calculate the relative intensity level between the reflected and transmitted signals.

The image at I is the object for a second converging lens. This second lens forms a final image at infinity with an overall angular magnification for the two lens arrangement of 5. Calculate the distance between the two converging lenses.

A new object is placed a few meters to the left of the original lens. The student adjusts spacing of the lenses to form a virtual image at infinity of the new object. Outline, without calculation, the required change to the lens separation.

Determine, by calculation, the linear magnification produced in the above diagram.

Explain the shape of the signal you sketched in (b)(ii).

In the ultrasound scan the frequency is chosen so that the distance between the transducer and the organ is at least 200 ultrasound wavelengths. Estimate, based on your response to (b)(ii), the minimum ultrasound frequency that is used.

The acoustic impedance of soft tissue is 1.65 × 106 kg m^-2 s^-1. Show that the speed of sound in the soft tissue is approximately 1500 m s^–1.

A physician has a range of frequencies available for ultrasound. Comment on the use of higher frequency sound waves in an ultrasound imaging study.

Suggest the advantage in medical diagnosis of using ultrasound of frequency 1 MHz rather than 0.1 MHz.

The fluid in the bowel has a similar linear attenuation coefficient as the bowel surface. Gases have much lower linear attenuation coefficients than fluids. Explain why doctors will fill the bowel with air before taking an X-ray image.

A parallel beam of X-rays travels through 7.8 cm of tissue to reach the bowel surface. Calculate the fraction of the original intensity of the X-rays that reach the bowel surface. The linear attenuation coefficient for tissue is 0.24 cm^–1.

When the Earth-Moon distance is 363 300 km, the Moon is observed using the telescope. The mean radius of the Moon is 1737 km. Determine the focal length of the mirror used in this telescope when the diameter of the Moon’s image formed by the main mirror is 1.20 cm.

Determine, in cm, the focal length of the objective lens.

Determine the distance at which the signal must be amplified.

Estimate the linear magnification of the image.

Explain chromatic aberration, with reference to your diagram in (b)(i).

Construct a ray diagram in order to locate the position of the image formed by the mirror. Label the image $\text{I}$.

Calculate, in cm, the distance between the eyepiece and the image formed by the objective lens.

In nuclear magnetic resonance (NMR) protons inside a patient are made to emit a radio frequency electromagnetic radiation. Outline the mechanism by which this radiation is emitted by the protons.

State and explain, with reference to you answer in (a)(i), what needs to be done to produce a clear image of the leg artery using X-rays.

Show that the ratio $\frac{I_{\mathrm{b}}}{I_{\mathrm{t}}}$ is close to 1.