Default please!!! help me connect my arc with my projector

I recently bought a pico projector OPTOMA PK101 from ebay without knowing that there is no composite/component out available in my xperia arc except for HDMI

now my problem is that i want to connect my phone with the projector and can someone please!!! help me. I am searching in many forums and the internet for this for almost a week now. I heard of some HDMI to rca converters but they are bulk and need a power source. Is there something similar to this available for my phone

also there is this accessory available for apple

is there a similar one like this which I can buy.

please please someone reply am desperate.

2)can my xperia arc convert digital signal to analog/composite so that I can connect cables like this