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Charlie
Let focal length of convex lens (glass) , f1 = 30cm
focal length of plane concave lens (liquid) is f2
and it is given that combined focal length , F =45cm
we know,
1/f1 + 1/f2 = 1/F [ combined focal length formula]
so, 1/f2 = 1/F -1/f1
1/f2 = 1/45 - /1/30
= (2 - 3)/90 = -1/90
f2 = -90cm
for lens (glass), R1 = R and R2 = -R
use lens make formula,
1/f1 = (u - 1)[1/R1 -1/R2]
1/30 = (3/2 - 1) [ 1/R + 1/R ]
1/30 = 1/2 × 2/R = 1/R
R = 30cm
now, for plane concave lens (liquid)
R1 = -R = -30cm , R2 = ∞
so, 1/f2 = (u' - 1)[1/R1 - 1/R2]
1/-90 = (u' - 1)[1/-30 - 1/∞]
-1/90 = (u' - 1)/-30
1/3 = u' - 1
u' = 4/3
hence, refractive index of liquid is 4/3
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