what is the purpose of condenser lens in a slide projector? What if we don't use any condenser lens? can't we use a single convex lens as a condenser? what difference will it make? kindly explain it in detail.
 A: The condenser lens systems collects light from divergent illumination sources, then redirects and condenses the light to flood the projector lens system. The classical condenser lens system consists of two PCX lenses mounted with their convex sides facing each other, as shown in the figure below. The first lens collects the divergent light cone from the illuminator (object or projector) and the second lens outputs the light as a convergent cone (image), which will illuminate the reticle.

Implicitly, the projection lens solution defines part of the condenser lens system, which is why designing the projection lens system first is crucial. The distance of the condenser lens system to the projector lens system is at least as great as the distance from the reticle to the projector lens system.
http://www.edmundoptics.com/resources/application-notes/optics/optics-application-examples/#application3

One could use a single convex element, however large angles of light from the source need to be collected for a sufficient lumen output which leads the designer to use two elements. The two elements facing each other also reduces spherical aberration.
A: The purpose of the condenser is to set up a highly defocussed lightfield through the object plane, i.e. the slide or LCD array. Ideally, the source used should be an extended one so that the lightfield at the slide is one of high optical grasp, so that the field at the object plane (slide) is like a whole bunch of broad apex angle (high numerical aperture) conical bundles of rays diverging from each point in that plane. The slide then imparts colored filtering to the high grasp field. The projection lens - the analogue of the objective in a microscope system - then images the slide plane onto the screen. It can do this because, thanks to the high grasp field, each pixel in the slide is like a point radiator.
One can partially get this effect by simply putting the slide some distance away from an extended light source such as a filament lamp or LED chip, and then imaging the slide plane. This would be like using the projector without a dedicated condenser. However, in that case, one has poor control over the intensity variation over the slide plane. Also the light grasp is often not as high in this case: the effective point radiators in the slide plane seem more like narrow pencils of light rather than cones. This second point is more important for microscope objectives, for it means that the full numerical aperture of the objective lens is not filled.
So, in summary, the condenser is (1) to control the distribution of illumination intensity across the object plane and (2), in the case of microscope objectives, increase the light grasp at that plane. Without the condenser, it is impossible to get a slide evenly lit. 
It turns out, just by co-incidence, that a good configuration of lenses for redistributing illumination light evenly across the object plane is a pair of plano-convex lenses with their apexes facing one another. More modern apsherics also do this job well: a well known property of aspherics is that they can be easily designed to redistribute the illumination intensity in their exit pupils, whereas spherical optics, at least low complexity ones, tend only to have a weak effect on illumination redistribution, and, from the standpoint of a projector, tend to worsen that distribution.
The Wikipedia article on Köhler Illumination explains all this.
A: 
What if we don't use any condenser lens? 

The condenser lens  which  consists of two  plano convex lens with their convex sides facing each other collects light from sources  which are usually divergent . 
It  redirects and condenses the  beam of light  to flood the projector lens system. 
In the classical condenser lens system the first lens of the pair  collects the divergent light coming from the illuminator (  source and  fibre optical guide system) and
the second lens outputs the light as a convergent cone (image), which will illuminate the reticle.
So, If one does not use a condenser lens then his projected image will be dim or low in intensity.

can't we use a single convex lens as a condenser?

The  idea of using two plano convex lenses in place of one convex lens is to enhance the collection of light intensity  coming from the illuminator and render it axially available  to the instrument.The placing of PCL with convex side facing each other is a definite advantage in focussing the light at the projection lens system.
The distance of the condenser lens system to the projector lens system is at least as great as the distance from the reticle(photo mask) to the projector lens system.
In brief the function of the condenser is to focus all the light that brightens the whole slide.
It also acts as a heat insulator to stop heat from the bulb so it does not spoil the slide.
In general condensers are/can be  utilized   in almost all  imaging devices, such as Microscopes, Enlargers, Slide projectors, Telescopes etc. .
The idea/technique  can be  applied to  to different  kinds of radiation also , e.g.  neutron radiation and synchrotron radiation optics  including electrons in electron  microscopy.
