How does Segwit achieve backwards compatibility in terms of the block size? If SegWit results in production of blocks that are larger than 1MB, how do old nodes see them as valid, instead of rejecting them due to exceeding the maximal allowed size of 1MB?
Segwit changes the definition of a maximum block size to be something called block weight. The maximum block weight is 4000000 weight units. We use the following formula to calculate the block weight:

3 * (size of non-witness data) + (size of everything including witness data)


So we can do some math here to figure out if the size of non-witness data will ever be more than 1 MB.

Let x = size of non-witness data
Let y = size of just witnesses
4000000 &gt;= 3x + (x + y)
4000000 &gt;= 4x + y
4000000 - 4x &gt;= y


Since this is just a downwards sloping line, the point at which y = 0 is where x will be the greatest. So setting y to 0:

4000000 - 4x &gt;= 0
-4x &gt;= -4000000
 x &lt;= 1000000


Thus the largest the non-witness data can be is 1 MB, which is exactly the maximum block size for non-segwit nodes. Since non-segwit nodes will only see the non-witness data, segwit is backwards compatible as blocks would still be within the size limit.