Uses of Polar Curves
Polar curves are made use of in determining the M.S.C.P. etc. of a source. They are also
used in determining the actual illumination of a surface i.e. while calculating the
illumination in a particular direction, the c.p. in that particular direction as read from the
vertical polar curve, should be employed.
Determination of M.S.C.P.and M.H.C.P. from Polar Diagrams
In Fig. 3.25 (a) is shown the polar distribution curve of a filament lamp in a horizontal
plane and the polar curve inFig. 3.25 (b) represents the c.p. distribution in a vertical plane.
It will be seen that the horizontal candle-power is almost uniform in all directions in that
plane.
However, in the vertical plane, there is a large variation in the candle power which falls to
zero behind the cap of the lamp. The curve in Fig. 3.25 (a) has been drawn with the help of
a photometer while the lamp is rotated about a vertical axis, say, 10° at a time. But the
curve in Fig. 49.25 (b) was drawn while the lamp was rotated in a vertical plane about a
horizontal axis passing through the centre of the filament.
Fig 3.24
The M.H.C.P. is taken as the mean of the readings in Fig. 49.25 (a). However, a more
accurate result can be obtained by plotting candle power on an angular base along the
rectangular axes and by determining the mean height of the curve by the mid-ordinate or by
Simpson‘s rule.
The M.S.C.P. of the lamp can be obtained from the vertical polar curve of Fig. 3.25 (b)
byRousseau‘s construction as explained below : Only half of the vertical polar curve is
shown in the figure (Fig. 49.26) since it is symmetrical about the vertical axis. With O is the
centre and radius OR equal to the maximum radius of the polar curve, a semi-circle LRM is
drawn.
A convenient number of points on this semi-circle (say 10° points) are projected onto any
vertical plane as shown. For example, points a,b,c etc. are projected to d,e,f and so on. From
point d, the horizontal line dg is drawn equal to the intercept OA of the polar diagram on the
radius oa. Similarly, eh = OB, fk = OC and so on. The points g, h, k etc., define the
Fig 3.25
Rousseau figure. The average width w of this figure represents the M.S.C.P. to the same scale
as that of the candle powers in the polar curve. The average width is obtained by dividing the
Rousseau area by the base of the Rousseau figure i.e. length lm which is the projection of the
semi-circle LM on the vertical axis. The area may be determined by Simpson‘s rule or by
using a plani meter
As explained earlier, the M.H.C.P. of an incandescent lamp can be easily obtained by
mounting the lamp with its axis vertical and taking photometer readings in the horizontal
plane while the lamp is rotated about its axis in steps of 10° or so. A definite ratio exists
between the M.H.C.P. and M.S.C.P. of each particular type of filament. M.S.C.P. of a lamp
can be found by multiplying M.H.C.P. by a factor known as spherical reduction factor which,
as defined earlier, is
For the particular lamp considered, f = 430/80 = 0.54 (approx.)