I downloaded an741 example for fpga 10M50. When I opened it in Quartus prime software, I was able to compile factory_image and app_image_1 but I am not getting any option to compile app_image_2. What to do?

I assumed you are talking about section 1.7.1.2, restore the Factory_image, application_image_1 and application_image_2, and compile all three designs.

https://www.intel.com/content/dam/www/programmable/us/en/pdfs/literature/an/an741.pdf

From the reference design given, add the appimage2.bdf in the project, set as top level and compile it.

Then you will get the top.sof file in the output_files. Rename the top.sof file to app_image2.sof or other preferred name.

You can do the same way with the factoryimage.bdf and appimage1.bdf. With that, all the .sof file will be generated.

Hope it helps.