Using the method of separation of variables and a new approach to calculations of the prolate spheroidal wave functions , we study the optical properties of very elongated ( cigar-like ) spheroidal particles .

A comparison of extinction efficiency factors of prolate spheroids and infinitely long circular cylinders is made .
For the normal and oblique incidence of radiation , the efficiency factors for spheroids converge to some limiting values with an increasing aspect ratio a / b provided particles of the same thickness are considered .
These values are close to , but do not coincide with the factors for infinite cylinders .
The relative difference between factors for infinite cylinders and elongated spheroids ( { { { { a / b \mathrel { \mathchoice { \vbox { \offinterlineskip \halign { \cr } $ \displaystyle > $ \cr% $ \displaystyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \textstyle > $ \cr$% \textstyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \scriptstyle > $ \cr$% \scriptstyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \scriptscriptstyle > $% \cr$ \scriptscriptstyle \sim$ } } } } 5 ) usually does not exceed 20 % if the following approximate relation between the angle of incidence \alpha~ { } ( { in~ { } degrees } ) and the particle refractive index m = n + ki takes the place : { { { { \alpha \mathrel { \mathchoice { \vbox { \offinterlineskip \halign { \cr } $ \displaystyle > $% \cr$ \displaystyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \textstyle > $ \cr$% \textstyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \scriptstyle > $ \cr$% \scriptstyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \scriptscriptstyle > $% \cr$ \scriptscriptstyle \sim$ } } } } 50 |m - 1 | +5 where { { { { { { { { 1.2 \mathrel { \mathchoice { \vbox { \offinterlineskip \halign { \cr } $ \displaystyle < $ \cr% $ \displaystyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \textstyle < $ \cr$% \textstyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \scriptstyle < $ \cr$% \scriptstyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \scriptscriptstyle < $% \cr$ \scriptscriptstyle \sim$ } } } } n \mathrel { \mathchoice { \vbox { \offinterlineskip% \halign { \cr } $ \displaystyle < $ \cr$ \displaystyle \sim$ } } } { \vbox { \offinterlineskip% \halign { \cr } $ \textstyle < $ \cr$ \textstyle \sim$ } } } { \vbox { \offinterlineskip \halign% { \cr } $ \scriptstyle < $ \cr$ \scriptstyle \sim$ } } } { \vbox { \offinterlineskip \halign { % \cr } $ \scriptscriptstyle < $ \cr$ \scriptscriptstyle \sim$ } } } } 2.0 and { { { { k \mathrel { \mathchoice { \vbox { \offinterlineskip \halign { \cr } $ \displaystyle < $ \cr$% \displaystyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \textstyle < $ \cr$% \textstyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \scriptstyle < $ \cr$% \scriptstyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \scriptscriptstyle < $% \cr$ \scriptscriptstyle \sim$ } } } } 0.1 .

We show that the quasistatic approximation can be well used for very elongated optically soft spheroids of large sizes .