Given:
Refractive index of the first medium, n1=1
Refractive index of the second medium, n2=1.4=57
Object distance, u=−4R
Radius of curvature of the spherical interface, R=+R (since the surface is convex towards the rarer medium)
Using the formula for refraction at a single spherical surface:
vn2−un1=Rn2−n1
Substituting the given values:
v1.4−−4R1=R1.4−1
5v7+4R1=R0.4
5v7+4R1=5R2
5v7=5R2−4R1
5v7=20R8−5=20R3
v=5×37×20R=328R
The transverse magnification m for a spherical refracting surface is given by:
m=n2un1v
Substituting the values of n1, n2, u, and v:
m=1.4×(−4R)1×(328R)
m=−528R328R
m=−35
The magnitude of the magnification is:
∣m∣=35≈1.66
Answer: 1.66