For refraction at a single spherical surface, we use the formula: vμ2−uμ1=Rμ2−μ1
Given data:
Refractive index of air μ1=1.0
Refractive index of glass μ2=1.5
Radius of curvature R=+50 cm (convex surface)
Object is at infinity for a parallel beam, so u=−∞
Substituting the values:
v1.5−−∞1.0=501.5−1.0
v1.5−0=500.5
v1.5=1001
v=1.5×100=150 cm
The image is formed at a distance of 150 cm from the pole (vertex) of the spherical surface.
The question asks for the distance x from the centre of curvature.
Distance from centre of curvature x=∣v−R∣
x=150−50=100 cm