NEW CARTESIAN SIGN ONVENTION
While dealing with reflection at spherical mirror, the following sign convention called New Cartesian Sign Convention is followed :
(i) All distances are measured from the pole of the mirror.
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| NEW CARTESIAN SIGN ONVENTION |
(ii) The distances measured in the direction of the incident light are taken as positive while those measured in the direction opposite to the incident light are taken as negative.
(iii) Heights or distances measured upward and perpendicular to the principal axis are considered positive while those measured downwards are considered negative.
According to this sign convention, the focal length (f) and radius of curvature (R) are negative for a concave mirror and positive for a convex mirror.
RELATION BETWEENS f AND R
f = R/2
,for a concave mirror as well as for a convex mirror.
,for a concave mirror as well as for a convex mirror.
MIRROR FORMULA
There is following simple relation between the distance u of the object from the mirror, the distance v of the image from the mirror and focal length f of the mirror :
There is following simple relation between the distance u of the object from the mirror, the distance v of the image from the mirror and focal length f of the mirror :
this is known as mirror formula and is valid for both concave and convex mirrors, whether the image formed is real or virtual However, the quantities must be substituted with proper signs.
Uses of concave mirrors
(i) A concave mirror is used as shaving or make-up mirror. It is because when the person keeps the face between the pole and focus of the concave mirror, a magnified and erect image of the face is formed.
(ii) A concave mirror is used by dental surgeons as inspection mirror to view the dental cavities.
(iii) A concave mirror is used as a reflector in headlights of cars, railway engines, search light etc. The source of light is placed at the focus of the concave mirror. The light rays after reflection travel over a large distance as a parallel intense beam.
(iv) A small concave mirror with a small hole at its centre is used in the doctor's ophthalmoscope. The concave mirror reflects the light on the retina of the patient. This makes the retina quite visible.
Uses of Convex mirrors
(i) A convex mirror is used as a driver's mirror in scooters, cars and other vehicles. The convex mirror produces virtual, erect and diminished images of the objects behind the vehicles. Therefore, the driver has a large field of view as compared to a plane mirror or concave mirror.
(ii) A convex mirror is used as a reflector in street lamps.
(iii) A convex mirror is used in anti-shoplifting devices.
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