What is the outer screen with the vertical ribs called on a tosiba tp55h60

That screen is called the linticular screen. Then inside screen is called the fresnel screen. Some times they are sold together and somethimes they are sold as each.

I usually order my parts from Andrews Electronics in California, they will have the OEM components that you will need.
Their site is http://www.andrewselectronics.com/welcome.aspx
And their phone number is a 24-Hour Order Desk: (800) 274-4666
I recommend the phone order so you can talk to the person about the different types of screens that are available, the price and availability.

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