SL Paper 3
A lamp is located 6.0 m from a screen.
Somewhere between the lamp and the screen, a lens is placed so that it produces a real inverted image on the screen. The image produced is 4.0 times larger than the lamp.
Identify the nature of the lens.
Determine the distance between the lamp and the lens.
Calculate the focal length of the lens.
The lens is moved to a second position where the image on the screen is again focused. The lamp–screen distance does not change. Compare the characteristics of this new image with the original image.
Spherical converging mirrors are reflecting surfaces which are cut out of a sphere. The diagram shows a mirror, where the dot represents the centre of curvature of the mirror.
A ray of light is incident on a converging mirror. On the diagram, draw the reflection of the incident ray shown.
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.
Optical fibres can be classified, based on the way the light travels through them, as single-mode or multimode fibres. Multimode fibres can be classified as step-index or graded-index fibres.
State the main physical difference between step-index and graded-index fibres.
Explain why graded-index fibres help reduce waveguide dispersion.
Both optical refracting telescopes and compound microscopes consist of two converging lenses.
Compare the focal lengths needed for the objective lens in an refracting telescope and in a compound microscope.
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.
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.
The diagram shows a schematic view of a compound microscope with the focal points fo of the objective lens and the focal points fe 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.
Image 1 shows details on the petals of a flower under visible light. Image 2 shows the same flower under ultraviolet light. The magnification is the same, but the resolution is higher in Image 2.
Explain why an ultraviolet microscope can increase the resolution of a compound microscope.
The diagram is a partially-completed ray diagram for a compound microscope that consists of two thin converging lenses. The objective lens L1 has a focal length of 3.0 cm. The object is placed 4.0 cm to the left of L1. The final virtual image is formed at the near point of the observer, a distance of 24 cm from the eyepiece lens L2.
Two converging lenses are used to make an astronomical telescope. The focal length of the objective is 85.0 cm and that of the eyepiece is 2.50 cm. The telescope is used to form a final image of the Moon at infinity.
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.
The distance between the lenses is 18 cm. Determine the focal length of L2.
On the diagram draw rays to locate the focal point of L2. Label this point F.
Explain why, for the final image to form at infinity, the distance between the lenses must be 87.5 cm.
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.
By reference to chromatic aberration, explain one advantage of a reflecting telescope over a refracting telescope.
The diagram shows planar wavefronts incident on a converging lens. The focal point of the lens is marked with the letter F.
Wavefront X is incomplete. Point Q and point P lie on the surface of the lens and the principal axis.
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).
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.
Communication signals are transmitted through optic fibres using infrared radiation.
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 dBkm–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.
Two converging lenses placed a distance 90 cm apart are used as a simple astronomical refracting telescope at normal adjustment. The angular magnification of this arrangement is 17.
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.
A beam of monochromatic light from infinity is incident on a converging lens A. The diagram shows three wavefronts of the light and the focal point of the lens.
Draw on the diagram the three wavefronts after they have passed through the lens.
Lens A has a focal length of . An object is placed to the left of A. Show by calculation that a screen should be placed about from A to display a focused image.
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 and the final real image is from the lens. Calculate the distance between lens A and lens B.
Calculate the total magnification of the object by the lens combination.
The graphs show the variation with time of the intensity of a signal that is being transmitted through an optic fibre. Graph 1 shows the input signal to the fibre and Graph 2 shows the output signal from the fibre. The scales of both graphs are identical.
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 dBkm–1.
A magnifying glass is constructed from a thin converging lens.
A converging lens can also be used to produce an image of a distant object. The base of the object is positioned on the principal axis of the lens at a distance of 10.0 m from the centre of the lens. The lens has a focal length of 2.0 m.
The object is replaced with an L shape that is positioned 0.30 m vertically above the principal axis as shown. A screen is used to form a focused image of part of the L shape. Two points P and Q on the base of the L shape and R on its top, are indicated on the diagram. Point Q is 10.0 m away from the same lens as used in part (b).
Sketch a ray diagram to show how the magnifying glass produces an upright image.
State the maximum possible distance from an object to the lens in order for the lens to produce an upright image.
Determine the position of the image.
State three characteristics of the image.
On the diagram, draw two rays to locate the point Q′ on the image that corresponds to point Q on the L shape.
Calculate the vertical distance of point Q′ from the principal axis.
A screen is positioned to form a focused image of point Q. State the direction, relative to Q, in which the screen needs to be moved to form a focused imaged of point R.
The screen is now correctly positioned to form a focused image of point R. However, the top of the L shape looks distorted. Identify and explain the reason for this distortion.
Outline the meaning of normal adjustment for a compound microscope.
Sketch a ray diagram to find the position of the images for both lenses in the compound microscope at normal adjustment. The object is at O and the focal lengths of the objective and eyepiece lenses are shown.
An optic fibre of length 185 km has an attenuation of 0.200 dB km–1. The input power to the cable is 400.0 μW. The output power from the cable must not fall below 2.0 μW.
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.
Calculate the maximum attenuation allowed for the signal.
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 λA and ray B has a wavelength of λB. 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.
A ray of light travelling in an optic fibre undergoes total internal reflection at point P.
The refractive index of the core is 1.56 and that of the cladding 1.34.
The input signal in the fibre has a power of 15.0 mW and the attenuation per unit length is 1.24 dB km–1.
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.
The refractive index of glass decreases with increasing wavelength. The diagram shows rays of light incident on a converging lens made of glass. The light is a mixture of red and blue light.
On the diagram, draw lines to show the rays after they have refracted through the lens. Label the refracted red rays with the letter R and the refracted blue rays with the letter B.
Suggest how the refracted rays in (a) are modified when the converging lens is replaced by a diverging lens.
Hence state how the defect of the converging lens in (a) may be corrected.
The diagram represents a simple optical astronomical reflecting telescope with the path of some light rays shown.
Identify, with the letter X, the position of the focus of the primary mirror.
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.
A radio telescope also has a primary mirror. Identify one difference in the way radiation from this primary mirror is detected.
The refractive index of a material is the ratio of the speed of light in a vacuum , to the speed of light in the material or .
The speed of light in a vacuum is 2.99792 × 108 m s-1. The following data are available for the refractive indices of the fibre core for two wavelengths of light:
Outline the differences between step-index and graded-index optic fibres.
Determine the difference between the speed of light corresponding to these two wavelengths in the core glass.
An input signal to the fibre consists of wavelengths that range from 1299 nm to 1301 nm. The diagram shows the variation of intensity with time of the input signal.
Sketch, on the axes, the variation of signal intensity with time after the signal has travelled a long distance along the fibre.
Explain the shape of the signal you sketched in (b)(ii).
A signal consists of a series of pulses. Outline how the length of the fibre optic cable limits the time between transmission of pulses in a practical system.
A ray diagram for a converging lens is shown. The object is labelled O and the image is labelled I.
Using the ray diagram,
determine the focal length of the lens.
calculate the linear magnification.
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.
An optic fibre consists of a glass core of refractive index 1.52 surrounded by cladding of refractive index n. The critical angle at the glass–cladding boundary is 84°.
The diagram shows the longest and shortest paths that a ray can follow inside the fibre.
For the longest path the rays are incident at the core–cladding boundary at an angle just slightly greater than the critical angle. The optic fibre has a length of 12 km.
Calculate n.
The refractive indices of the glass and cladding are only slightly different. Suggest why this is desirable.
Show that the longest path is 66 m longer than the shortest path.
Determine the time delay between the arrival of signals created by the extra distance in (b)(i).
Suggest whether this fibre could be used to transmit information at a frequency of 100 MHz.
A small object is placed at a distance of 2.0 cm from the objective lens of an optical compound microscope in normal adjustment.
The following data are available.
Magnification of the microscope = 70
Focal length of the eyepiece = 3.0 cm
Near point distance = 24 cm
State what is meant by normal adjustment when applied to a compound microscope.
Calculate, in cm, the distance between the eyepiece and the image formed by the objective lens.
Determine, in cm, the focal length of the objective lens.
A converging (convex) lens forms an image of an object on a screen.
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.
Communication signals are transmitted over long distances through optic fibres.
A signal is transmitted along an optic fibre with attenuation per unit length of 0.40 dB km–1. The signal must be amplified when the power of the signal has fallen to 0.02 % of the input power.
Describe why a higher data transfer rate is possible in optic fibres than in twisted pair cables.
State one cause of attenuation in the optic fibre.
Determine the distance at which the signal must be amplified.
The diagram shows two light rays that form an intermediate image by the objective lens of an optical compound microscope. These rays are incident on the eyepiece lens. The focal points of the two lenses are marked.
The object O is placed at a distance of 24.0 mm from the objective lens and the final image is formed at a distance 240 mm from the eyepiece lens. The focal length of the objective lens is 20.0 mm and that of the eyepiece lens is 60.0 mm. The near point of the observer is at a distance of 240 mm from the eyepiece lens.
Draw rays on the diagram to show the formation of the final image.
Calculate the distance between the lenses.
Determine the magnification of the microscope.
A student places an object 5.0 cm from a converging lens of focal length 10.0 cm.
The student mounts the same lens on a ruler and light from a distant object is incident on the lens.
Construct rays, on the diagram, to locate the image of this object formed by the lens. Label this with the letter I.
Determine, by calculation, the linear magnification produced in the above diagram.
Suggest an application for the lens used in this way.
Identify, with a vertical line, the position of the focussed image. Label the position I.
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.
The diagram, drawn to scale, shows an object O placed in front of a converging mirror. The focal point of the mirror is labelled F.
A planar wavefront of white light, labelled A, is incident on a converging lens. Point P is on the surface of the lens and the principal axis. The blue component of the transmitted wavefront, labelled B, is passing through point P.
Construct a ray diagram in order to locate the position of the image formed by the mirror. Label the image .
Estimate the linear magnification of the image.
Describe two features of the image.
Sketch, on the diagram, the wavefront of red light passing through point P. Label this wavefront R.
Explain chromatic aberration, with reference to your diagram in (b)(i).
An achromatic doublet reduces the effect of chromatic aberration. Describe an achromatic doublet.
An astronomical reflecting telescope is being used to observe the night sky.
The diagram shows an incomplete reflecting telescope.
Complete the diagram, with a Newtonian mounting, continuing the two rays to show how they pass through the eyepiece.
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.
The final image of the Moon is observed through the eyepiece. The focal length of the eyepiece is 5.0 cm. Calculate the magnification of the telescope.
The Hubble Space reflecting telescope has a Cassegrain mounting. Outline the main optical difference between a Cassegrain mounting and a Newtonian mounting.
A single pulse of light enters an optic fibre which contains small impurities that scatter the light. Explain the effect of these impurities on the pulse.
The diagram represents a diverging mirror being used to view an object.
Construct a single ray showing one path of light between the eye, the mirror and the object, to view the object.
The image observed is virtual. Outline the meaning of virtual image.