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Patent Searching and Data


Title:
IMPROVEMENTS IN OPTICAL DEVICES
Document Type and Number:
WIPO Patent Application WO/1998/033078
Kind Code:
A1
Abstract:
A device for deflecting and/or extending a person's field of view to enable that person to see round obstructions in his/her field of view comprising a bar prism having at least one concave face. The device is provided in a kit form for application onto a window, windscreen or mirror or the like or forms an integral part of same. In the case of its application with respect to windows when positioned adjacent a window frame in the field of view of a person the device enables that person to see objects which would normally be obscured by the frame. In the case of its use on a mirror the device significantly expands the field of view of a person e.g. a driver of a vehicle.

Inventors:
HOPKINS DAVID (GB)
Application Number:
PCT/GB1997/000205
Publication Date:
July 30, 1998
Filing Date:
January 23, 1997
Export Citation:
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Assignee:
HOPKINS DAVID (GB)
International Classes:
B60R1/08; B60R1/10; G02B5/04; G02C7/14; (IPC1-7): G02B5/04; B60R1/08
Foreign References:
EP0497445A11992-08-05
DE2914361A11980-10-23
US5245479A1993-09-14
US4182552A1980-01-08
US5579133A1996-11-26
US3726586A1973-04-10
Attorney, Agent or Firm:
BAILEY WALSH & CO. (Leeds LS1 2SD, GB)
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Claims:
The claims
1. A device for deflecting and/or extending a field of view comprising a bar prism having at least one concave face.
2. A device in accordance with claim 1 wherein the or each concave face of the device may comprise a substantially planar portion having at least one concave edge or may be substantially concave or any appropriate variation between these two alternatives.
3. A device in accordance with claim lor 2 wherein, the prism has a front face and a rear concave face which form the wedge shape of the prism and that the concave face curves smoothly from the wider end of the wedge, where the front face is at the greatest angle to the rear face, to the narrower end, where the front face is parallel to the rear face.
4. A device in accordance with claim 2 wherein the prism has a front face and a rear concave face which form the wedge shape of the prism and the rear face is defined by a first planar section lying at a fixed angle to the front face and extending from the wider end of the wedge to a position close to but short of the narrower end, and a second planar section lying parallel to the front face and extending from the said position to the narrower end, the said two sections being interconnected by a small radiussed or curved fillet to prevent a sharp step from being formed in the image as it moves from the first section to the second section.
5. A device in accordance with either of claims 3 or 4 wherein the front and rear faces forming the said narrower end of the prism are substantially parallel such that there is no change in the appearance of the image as it moves beyond the narrower end of the prism into the viewer's line of vision which is clear of the prism.
6. A device in accordance with any preceding claim wherein the prism is located to the side section of the viewer's field of view, with the wider end of the prism located further to the side than the narrower end.
7. A device in accordance with any of claims 16 wherein the cross sectional shape of the bar prism is varied along its length.
8. A device in accordance with any preceding claim wherein the prism is made from a transparent material comprising glass and/or a transparent or semitransparent plastic/polymer 9) A device in accordance with claim wherein the plastic or polymer may comprise any one or more of, , a polycarbonate, polyvinyl chloride (PVC), silicone Rubber, polysulphone, polymethyl methacrylate (PMMA), acrylic polymers, ehtylene vinyl acetate(EVA) copolymers, polyethylene and/or polypropylene plastomer, polystyrene, styrene acrylonitrile (SAN) copolymer, cellulose acetate butyrate (CAB), cellulose acetate proprionate (CAP), cellulose acetate (CA), styrene copolymers, polyethylene, polypropylene homo and copolymers, acrylonitrile styrene acrylonitrile (ASA), ethylene methyl acrylate (EBA), thermoplastic elastomer (TPE), thermoplastic rubber (TR), polyvinylidene dichloride(PVDC) or TPX.
9. A device in accordance with any preceding claim wherein the prism is adapted to be mounted onto a transparent support or onto a mirror.
10. A device in accordance with claim 10 wherein the prism is mounted on a transparent support or mirror or the like by self adhesion or using any appropriate adhesive which will not affect vision through the prism and window or mirror or the like.
11. A device in accordance with claim 11 wherein the adhesive is a glue or adhesive which is colourless and transparent upon hardening.
12. A device in accordance with any of claims 19 wherein the prism is an integral part of a transparent support or a mirror.
13. A device in accordance with any one of claims 1013 wherein the transparent support is glass or the like.
14. A device in accordance with claim 12 wherein the glass or the like is an optical lens, window or vehicle windscreen or the like.
15. A device in accordance with claim 1013 wherein the mirror is a vehicle rear view mirror or wing mirror.
16. A device in accordance with any of claims 115 wherein the prism is positioned on a window of a vehicle adjacent an obstruction in a driver's field of view in order to enable the driver to see around the obstruction.
17. A device in accordance with any of claims 113 or 16 wherein the prism is situated along an edge of a wing mirror of a vehicle to increase the viewing capability of the driver about the side of the vehicle.
18. A device in accordance with any of claims 115 wherein the prism is positioned on one or more optical lenses or the like to relieve phorias and/or overcome double vision from extra ocular muscle palsies and pareses and/or to extend a field of vision into blind spot areas (scotomata).
19. A window, windscreen, optical lens or mirror comprising one or more devices in accordance with any preceding claim 21) A vehicle having one or more devices according to the present invention located in at least one window and/or on at least one mirror thereof.
20. A pair of spectacles comprising at least one optical lens in accordance with claim 19.
21. A kit of parts comprising a device in accordance with any one of claims 110 and one or more adhesives suitable for adhering the prism to a window or mirror or the like.
22. A device for enabling a viewer to see round an obstruction in a viewer's field of vision to view persons or objects which would normally be obscured by such obstruction, characterised in that the device comprises a curve faced bar prism of which the two faces forming the wedge shape are transverse to the viewer's field of vision, and the wider end of the wedge is for location adjacent the obstruction.
23. A device as hereinbefore described with reference to the drawings.
Description:
Improvements in Optical Devices This invention relates to refracting optical devices for deflecting fields of view and relates particularly but not exclusively to optical devices for deflecting a field of view which may contain a person, a vehicle or other obstacle. For example the device may be used in a vehicle to allow the driver to view areas which are usually obscured from view, and for safety screens to enable people to see round obstructions eg in a bank, and in the window of a building in order to enable an occupant to ascertain who is at the house door.

There are a wide variety of devices which have been invented to enable a driver of a vehicle to see around obstructions or widen his field of view. Most of these devices are adapted to increase the field of view of the driver through the rear window or rear flanks of the vehicle being driven. Usually these devices take the form of mirrors or of Fresnel prism lens based systems. A device using a series of prisms has been invented as a more aerodynamic alternative to using wing mirrors.

The mirror based systems for widening the field of view of the driver have involved the use of convex mirrors which are usually adhered to standard wing mirrors and/or the internal rear view mirror of the vehicle.

Examples of systems using Fresnel prism lenses are described in PCT Publication No WO 82/04229, which discloses a Fresnel prism lens having a negative focal length, GB 1418045, which discloses examples of Fresnel prism lenses and prisms for expanding and deflecting fields of view and GB 1300540, which discloses a vehicle rear view mirror which is optically equivalent to a convex mirror and is in the Fresnel form.One major problem in relation to Fresnel prism lens devices is that any object viewed through such a device is significantly blurred and degraded.

Furthermore, there are a number of additional areas of restricted view in a vehicle other than the rear window and the rear flanks. In particular the sides of windscreen frames and side and rear window frames create blind spots. Of particular importance are the sides of a windscreen frame which may obscure a pedestrian, cyclist or a vehicle from a drivers field of view. This is of particular importance when a vehicle is about to move from a stationary position i.e. when it is about to move from a parked position or when it is at a junction preparing to enter a main road or at a pedestrian crossing.

The present invention comprises a device for deflecting and/or extending a person's field of view to enable that person to see round obstructions in his/her field of view comprising a bar prism having at least one concave face.

A concave faced bar prism is used in the present invention as a conventional bar prism would enable a person to see around obstructions but would itself produce a blind spot.

The or each concave face of the device may comprise a substantially planar portion having at least one concave edge or may be substantially concave or any appropriate variation between these two alternatives.

The device can be made to any appropriate length, width thickness or concavity and can be mounted onto a window or windscreen or the like or onto a rear view mirror or side mirror in for example the case of vehicles and the like. In a preferred embodiment a device of the present invention may be fixed onto a window or the like in a position parallel and/or adjacent an obstruction to enable a person to see around the obstruction such as the side of a window frame.

The use of such a device in this situation overcomes the significant problem for a driver of an obscured field of view due to the presence of sides to windscreen frames in vehicles as the device when appropriately fixed to the windscreen enables the driver to see around the frame.

Furthermore when a device of the present invention is applied onto a mirror the device will provide a greatly increased range of view for, for example, a driver in a car and will therefore overcome problems caused by blind spots around the rear flanks of a vehicle.

Furthermore when compared with the image seen by a driver using a wing mirror having a convex mirror adhered thereto the actual image viewed is clearer and better defined and is therefore more suitable for assisting a driver.

In a still further embodiment a spectacle based device of the present invention may be utilised as an ophthalmic aid for example by relieving phorias and overcoming double vision from extra ocular muscle palsies and pareses and for extending the field of vision into blind spot areas (scotomata).

The device may be mounted on a window, mirror or optical lens or the like by self adhesion or using any appropriate adherent which will not affect vision through the prism and window, mirror or optical lens or the like. Preferably, the adherent is a clear glue or adhesive which is colourless and transparent upon hardening.

Alternately, the device may form an integral part of a windscreen, window or mirror or the like . This has the advantage that the view through the prism and windscreen, window or mirror etc. will not be obscured bv any adhesive used and will ensure that the prism will not become detached from or move relative to a window over an extended period of time.

The cross-sectional shape of the bar prism of the invention may be varied in order to ensure the best view for the driver around each obstruction in a vehicle or into restrictive fields of view. The shape may vary within the length of a concave faced bar prism to reduce distortion associated with windscreen and/or mirror slope. Hence a vehicle may have a series of prisms situated adjacent different obstructions and on various mirrors and the cross-sectional shape of each prism will be adapted to provide the best possible, least distorted, view around the obstruction or extension of view through a mirror.

The device according to the invention is preferably therefore located along a side of a window of a vehicle and is adapted to enable the driver of the vehicle to see around an obstruction such as the side or lower edge of the window.

The invention further comprises a vehicle having one or more devices according to the present invention located in at least one window and/or on at least one mirror thereof.

The device may be made of any appropriate transparent material having an appropriate refractive index, but is preferably made from glass or a transparent or semi-transparent plastic/polymer The plastic or polymer may comprise any one or more of, for example, a polycarbonate, polyvinyl chloride (PVC), silicone Rubber, polysulphone, polymethyl methacrylate (PMMA), acrylic polymers, ehtylene vinyl acetate(EVA) copolymers, polyethylene and/or polypropylene plastomer, polystyrene, styrene acrylonitrile (SAN) copolymer, cellulose acetate butyrate (CAB), cellulose acetate proprionate (CAP), cellulose acetate (CA), styrene copolymers, polyethylene, polypropylene homo and copolymers, acrylonitrile styrene acrylonitrile (ASA), ethylene methyl acrylate (EBA), thermoplastic elastomer (TPE), thermoplastic rubber (TR), polyvinylidene dichloride (PVDC) and TPX.

The transparent material may be varied in any one of the following ways to provide an optimum curve faced bar prism namely transparency, colour, refractive index, softness, rigidity, density, plasticity, pliability, flexibility, memory, elasticity and adhesiveness.

In a further embodiment the present invention comprises a device for enabling a viewer to see round an obstruction in the viewer 5 field of vision to view persons or objects which would normally be obscured by such obstruction, characterised in that the device comprises a curve faced bar prism of which the two faces forming the wedge shape are transverse to the viewer's field of vision, and the wider end of the wedge is for location adjacent the obstruction.

By this means, it is provided that light rays from behind the obstruction are deflected, in passing through the curve faced prism, in a direction away from the narrow end of the wedge and onward to the observer, enabling any person or object in the region behind the obstruction to be seen.

The said faces of the wedge prism preferably comprise a front face which faces away from the viewer, when in use and a rear face from which light rays from an object in the viewer 5 lines of vision emerge, and those which pass through increasingly thicker parts of the prism, are deflected increasingly away from the narrower end of the wedge.

At the said narrower end the said faces are preferably substantially parallel such that the lines of the viewer's vision are not deflected, so that any image, for example a person moving into the viewer 5 field of view, in a direction from the wider end of the prism to the narrower end of the prism, will first of all be seen when behind the obstruction, although distorted by the abovementioned deflection of the viewer's lines of vision at that part of the prism, and will continue to be seen as he or she moves progressively across the viewer's line of vision through the prism.

When the person moves across the viewer's line of vision at the narrower end of the prism, as the viewing lines are not deflected, the image will cease to be distorted, and there will be no change in the appearance of the image as it moves beyond the narrower end of the prism into the viewer's line of vision which is clear of the prism, and therefore the image moves "seamlessly" from the narrower end of the prism into the viewer's line of vision which is clear of the prism.

The location of the prism in relation to the field of view therefore may be an important consideration, and preferably the prism is located to the side section of the viewer's field of view, with the wider end of the wedge located further to the side than the narrower end.

The invention in particular embodiments comprises the combination of a means for mounting a prism or a number of such prisms in relation to a location for occupation by a person or persons, and wherein at said location or locations, there is a field of view obstruction associated with the or each prism, and the associated prism is mounted with the wider end nearer the associated obstruction.

In one example, the prism is mounted on or adjacent or in the windscreen of a motor vehicle, at the side thereof, with the prism adjacent the window frame, which forms the obstruction. There may be two of said prisms, one at each side of the windscreen, and symmetrically or asymmetrically arranged. Other similar prisms may be located adjacent other blind spots of the vehicle. There are many other instances where the invention can be used. It can be used in banks and building societies where counter personnel may require to view customers without being seen themselves. It can be used in glazed operator cabins, such as are employed in cranes, hoists, chair lifts and the like. It can also be used in domestic dwellings and offices for security purposes, as it can be used to view people who are outside without the viewer inside the house or office being seen.

The invention also resides in the arrangement of the prisms when in the in use position.

As to the said faces of the prism which form the wedge, the rear face is preferably planar, and the front face in a preferred arrangement, is preferably concave, curving smoothly from the wider end of the wedge, where the front face is at the greatest angle to the rear face, to the narrower end, where the front face is parallel to the rear face, to provide the "seamless" movement of the images as discussed above.

In another arrangement, the front face is defined by a first planar section lying at a fixed angle to the rear face and extending from the wider end of the wedge to a position close to but short of the narrower end, and a second planar section lying parallel to the rear face and extending from the said position to the narrower end. The said two sections are preferably connected by a small radiussed or curved fillet to prevent a sharp step from being formed in the image as it moves from the first section to the second section.

The front and rear faces of the prism adjacent the apex or narrow end of the wedge are preferably "parallel". That is to say, if a cross section were taken through the prism along any line of vision of the viewer, the section lines of the front and rear face would be parallel.

The prism of the present invention may be supplied as a single self adherent unit for application onto an appropriate surface or may be supplied in the form of a kit comprising a prism and one or more adhesives for adhering the prism to a window or mirror or the like or may comprise an integral part of a window or mirror unit.

Embodiments of the invention will now be described by way of example, with reference to the accompanying drawings, wherein;- Fig. 1 is a perspective view of a wedge prism according to one embodiment of the invention; Fig. 2 is an edge view of the prism shown in Fig. 1; Fig. 3 shows how the prism of Fig. 1 is used in relation to the field of vision of a viewer; Fig. 4 illustrates what is seen by the viewer in Fig. 3 in four respective object positions A, B, C and D; Fig. 5 is a view similar to Fig. 2 but showing alternative arrangement; Fig. 6 shows the optical arrangement which applies in using the prism shown in Fig. 5; Fig.7 shows an alternative embodiment of the present invention wherein the prism is attached to a vehicle wing mirror.

Fig. 8 is an optical plan view showing how the prism is used in relation the wing mirror of Fig. 7.

Figs.9a and b show the increased area visible to a person when using a modified wing mirror in comparison to a standard planar wing mirror.

Fig. 10 is an illustration of the blind spots at the side of a normal car which are beyond a drivers peripheral vision Referring to the drawings, and firstly to Fig. 1, a wedge prism of constant cross section is shown, and it comprises a front face 2 a rear face 4 a wide end face 6 and a narrow end face 8. The faces 2 and 4 are the faces which define the angle or approximate angle/shape of the wedge, and in use a viewer looks through the prism in a direction from the front face 2 to the rear face 4. The front and rear faces may be appropriately shaped in that they may be planar or curved, and in Fig. 1 the front face 2 is curved in a concave fashion, whilst rear face 4 is planar, as shown more clearly in Fig. 2.

The curvature of front face 2 is such that at the narrow end 8 a front face 2 and rear face 4 are substantially parallel, whilst at the wide end 6 the front face lies at the sharpest angle to the rear face.

As the viewer looks through the prism in the manner described, so therefore light rays from an object at the wider edge of the prism will tend to be most refracted as they pass through the prism and specifically in relation to Fig. 2, these rays of light will refract to the right.

At the narrow end 8 however these lines of vision will be undeflected as explained further to Fig. 3 which shows how the prism is used. In this figure, an obstruction 10 is illustrated which may be for example a window frame or the edge of the windscreen of the vehicle, and the eye 12 illustrated in Fig. 3 may be the eye of a driver of the vehicle. The prism is positioned as shown with wide end 6 adjacent obstruction 10 and by virtue of the relative refraction of the rays of light from an object to the eye as they pass through the prism, so a region which is indicated by reference 14 and which is normally a blind spot, behind the obstruction 10, can be viewed.

The effective advantage of the prism can be best explained in considering the movement of an object or person 16 across the field of vision of the viewer 12. Assume that object 16 is initially at position A and is directly visible by the viewer as indicated by rays of light 18 which pass to the right of the obstruction 10. As object 16 moves in the direction of the arrow 20 it moves into the blind spot region 14 as shown in position B, but it still will be observed by the viewer because the rays of light such as 22 which pass through the broad end of the prism wedge are refracted to the right and object 16 can therefore still be seen.

Object 16 will appear somewhat distorted as shown at B in Fig. 4 because of the refraction of the lines of vision, but nevertheless it will still be visible to the viewer 12. As object 16 continues its movement from B towards C it will continue to be seen by the viewer and when it reaches position C where half of it is visible through the narrow end of the prism wedge 8, and half of it is visible directly by the viewer past the end of the wedge as indicated by lines of vision 24 and 26, there will be little or no distortion in that portion of the image which is viewed through the narrow end 8 of the prism because at that end the front and rear faces 2 and 4 are substantially parallel.

When object 16 moves finally to position D it will be again directly visible by the viewer through rays of light 28 and it will again in this case appear undistorted. Respective images seen by the viewer corresponding to positions A, B, C and D of the object 16 are shown in Fig. 4, and it will be seen that at position A it may well be that an edge 30 of object 16 is also seen from the left hand side of the obstruction 10, depending on the form of the prism.

Because the faces at the narrow end 8 are designed so as to be substantially parallel, the image seen by the viewer as it moves from the prism into direct vision moves "seamlessly" past the narrow end of the prism.

The device provides an extremely effective means of enabling the viewing of a blind spot which would not otherwise be viewable by for example a driver of a motor vehicle.

Fig. 5 illustrates an alternative form of wedge prism which operates in the same manner as described in relation to Fig. 3 except that the front face 2 is made up of two planar sections 2A and 2B. Section 2A is inclined relative to rear face 4 as shown to a position 32 adjacent the narrow end 8 of the prism, and section 2B is parallel to the rear face to provide the seamless movement effect described above. The region 32 may be radiused slightly in order that there will be no abrupt change in the image.

In the arrangement of Fig. 2, the image will tend to remain distorted until it reaches region 32 whereas in the arrangement of Fig. 2, the distortion of the image is progressively reduced as the image moves across the prism. Fig. 6 shows in a view similar to Fig. 3 how the prism shown in Fig. 5 operates optically such that much less distortion of an image will occur in the prism of Fig. 5 than the prism of Fig. 6.

Fig. 7 shows an alternative use for the curve faced bar prism of the present invention which is a means of reducing blind spots outside the peripheral vision of a person by application of the prism onto vehicle mirror. The mirrors in question may of course be either the rear view type or as shown in fig. 7 wing mirrors. Wing mirror 50 comprises planar mirror 52, holder 54 and an attachment means 56 for attaching mirror 50 to the side or wing of the vehicle in question. A curve faced bar prism 58 is fixed to the edge of mirror 52 remote from the vehicle body (not shown). Figs 7a and b are cross-sectional views of the mirror in Fig.7 along the line A-A and show that the Prism 58 may be a separate unit 58a adapted to be adhered to the planar mirror by a person who might buy the prism in a kit form or forms an integral part of planar mirror 52.

Fig. 8 shows a planar mirror 52 at one end of which is fixed a curve faced bar prism 58. The arrows directed towards prism 58 show rays from an object in the field of view of the driver because of the presence of prism 58 on mirror 52. Ray 73 is incident on mirror 52 at a point 75 where prism 58 is substantially planar and therefore it is reflected by the mirror 52 under the usual Laws of reflection. Ray 71 however is incident on prism 58 at position 62 which is where lens 58 is almost at its thickest and as such the ray is refracted by prism 58 before reflection on the mirror at point 60 and then subsequently leaves the prism at point 64 which is at a point where the prism is less thick and therefore the refraction caused by the prism increases the field of vision available to a driver through his wing mirror.

Figs. 9a and b are comparisons showing the fields of view with respect to the eyes of a driver 80,82 when using a standard planar wing mirror 52 (Fig. 9a) and a modified wing mirror 52,58 of the type described by the present invention (Fig. 9b). Referring initially to Fig. 9a virtual monocular images for the right and left eyes of a driver 80a and 82a are shown behind mirror 52 together with the virtual ambinocular image which is the virtual image of the both eyes when looking at the same object at the same time. The angle of vision of left eye 82 is indicated by the arrows 86. The angle of vision of the right eye 80 is indicated by arrows 88 and hence the binocular angle of vision i.e. the angle vision seen by both eyes is indicated by arrows 84 and the ambinocular angle of vision i.e. the maximum angle of vision of both eyes is indicated by arrows 90. It will be seen that the ambinocular angle of vision 90 is a relatively small acute angle.

In comparison with reference to Fig 9b wherein mirror 52 is provided with a curve faced bar prism 58, the effect of the refraction of rays through the prism 58 is significant creating a much greater angle of ambinocular vision 90a which may be as large as 50° when measured from the side of the drivers ear.

Fig. 10 shows the difference between the use of a planar mirror 52, the use of a convex mirror and the use of a prism 58 attached to a planar or convex mirror 52 when each of the above alternatives forms the wing mirror for a vehicle, which in the example provided is a car on a motorway. It will be seen that the motorway in Fig. 10 comprises a hard shoulder 100 and an inner, middle and outer lanes 102, 104 and 106 respectively. Typically in the UI( the width of the hard shoulder is in the region of 3.5 m wide and each of the other lanes are approximately 4 m wide.

The Figure shows a car 108 in lane 102 being over taken by another car 110 in lane 104. In the present diagram the wing mirror is depicted by the letter M and merely identifies the position of the mirror on the car body and line MD is an extension of the side of the body of car 108 on which mirror M is fixed.

The angle DMC typifies the field of view of a driver 112 in car 108 when mirror M is a standard planar mirror. As will be seen from the line MC by looking through the mirror M alone car 110 is not visible to driver 112 and as such the driver 112 may pull out from lane 100 into lane 102, oblivious to the presence of overtaking car 110, and cause an accident by crashing into the overtaking car. This is because car 110 is positioned totally in the blind spot of driver 112 i.e. within the area within angle AMC which indicates the peripheral view of the driver when reliant on the planar mirror for rear side view. Hence driver 112 has a significant blind spot on his right flank in which area he is unable to see overtaking traffic.

In the case when mirror M takes the form of a convex wing mirror, the field of view of driver 112 is improved to a certain degree as the field of view is depicted by the angle formed by the lines DMB. In this case it is to be noted that the near side rear wing of the overtaking car may just be visible to give to the driver if he is sufficiently observant and certainly the increased field of vision provides driver 112 with an improved chance of seeing the overtaking car during the early part of the overtaking movement.

However, it is to be noted that there is still a significant blind spot in the area provided by the angle AMB.

However, a mirror M comprising a planar or convex mirror section and a curve faced bar prism of the present invention significantly improves the field of view as such a wing mirror will enable a driver 112 to have a significantly reduced blind spot in that he will be able to see another vehicle in the area within angle DMV and as such most of the overtaking car 110 in lane 104 is visible to a driver 112 in car 108 and as such driver 112 is significantly less likely to move into lane 104 whilst car 110 is overtaking it. Angle DMV is in the region of 50°. Hence it will be noticed that the size of the blind spot shown as the area within angle AMV smaller than in the cases of the blind spot of the planar or convex mirrors previously discussed is significantly reduced.