Hello Arumalpra,
first of all, OSPF has no backup path concept like we can find in EIGRP. If a link fails in the area the router(s) connected to the failed link generate a new Router LSA stating the state of the link as down. The LSA(s) is flooded in the area all routers run SPF and eventually make changes to the IP routint table for one or more destinations.
In other words, finding the alternate path is the main job of OSPF routing protocol.
As a human being operator you can examine the OSPF database looking for information about an alternate path.
Because the OSPF database is unique and synchronized in all routers that are members of the same OSPF area you don't need to examine the OSPF database of all routers in the OSPF area.
The OSPF database is quite complex so an approximated workaround could be the following:
perform a traceroute from initial router to final destination, the traceroute shows the current OSPF best path installed in OSPF routers and shows the router hops in the path.
Connect in telnet/SSH to each router hop and list the OSPF neighbors, an alternate path can exist only if the topology provides it.
If there are some router hops with more then 2 OSPF neighbors an alternate path may exist.
examining the OSPF database
You can start by looking at the router LSA of the router that advertises the destination (the penultimate in the traceroute)
show ip ospf router
(but the OSPF routerid is not the same as penultimate IP address in traceroute here is the key point)
to find the OSPF router-id you can connect to the last router using the penultimate address in traceroute and do show ip ospf the OSPF router id is listed in the output.
The router LSA provides a list of all the links in the same area and you can learn of OSPF neighbors and so of possible alternative paths.
But some training is required to read the OSPF database
see
http://www.cisco.com/en/US/docs/ios/12_3t/ip_route/command/reference/ip2_s4gt.html#wp1159363
Hope to help
Giuseppe
