Solution
With no mica seventh bright fringe corresponds to path difference = dsin ? = 7 ?
with one slit covered, there is an additional path difference due to change of ?` = ?/n in the mica
Let unknown thickness of mica be L
path difference in mica compared to no mica is [L/ ?` - L/ ?] ? = [nL -L] = [1.58L - L] =.58L
to shift seventh bright fringe to center, this must correspond to 7 ? = .58 L
hence L= 7 ? /(.58) = 7(550)x10-9/.58 = 6.64?m