As per the given question,
Let the focal length of the lens 1 is f1 and focal length of the lens 2 is f2,
R1=8cm,R2=2cm,R1′=∞,R2′=(10+R)
R=4
a) We know that
f11=R11+R21
f11=−81−21=8−5
So, f1=5−8=−1.6cm
Similarly,
f21=R1′1+R2′1=∞1+−141
Hence focal length of the lens 2 will be f2=−14cm
b) Net focal length fnet
fnet1=f11+f21+f1f2d
Now, substituting the values,
fnet1=−1.61+−141+1.6×1418−12
fnet1=−(1.6×1414+1.6−6)=22.4−9.6=7−3
fnet=3−7cm
Object is at origin, so u =12cm, let the final image is at v,
v=fnet+ufnetu=−12−3−73−7×(−12)=−4384=−1.95cm
c) M=v/u=−1.95/(−12)=0.1625
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