1. Given data

• Diameter of spherical globe: $30\text{ cm}$
• Radius: $R = 15\text{ cm}$
• Refractive index of globe: $\mu = 1.5$
• Incident light: parallel beam, so object is effectively at infinity.

We need the point where the rays converge after refraction through the transparent sphere.

2. Use refraction at a spherical surface for the first surface

For refraction at a spherical surface,

For the first surface:

• Medium of incidence: air, so $\mu_1 = 1$
• Refracted medium: glass, so $\mu_2 = 1.5$
• Object at infinity: $u = -\infty \Rightarrow \frac{1}{u}=0$
• Radius of first surface: center is to the right, so $R = +15\text{ cm}$

Thus,

So,

This means the first surface alone would form an image $45\text{ cm}$ to the right of the first surface.

3. Use this image as object for the second surface

The two surfaces are separated by the diameter:

So relative to the second surface, the image formed by the first surface lies:

to the right of the second surface.

Hence for the second surface, this acts as a virtual object at distance

(on the right side of the second surface).

For the second surface:

• Incident medium: glass, so $\mu_1 = 1.5$
• Refracted medium: air, so $\mu_2 = 1$
• Object distance: $u_2 = +15\text{ cm}$
• Radius of second surface: center is to the left, so $R_2 = -15\text{ cm}$

Apply the formula:

Simplify:

Therefore,

So the beam converges at a point $7.5\text{ cm}$ to the right of the second surface.

4. Distance from the centre of the globe

The center of the globe is $15\text{ cm}$ from the second surface. Since the image is $7.5\text{ cm}$ to the right of the second surface, its distance from the center is

Convert to mm:

5. Final answer

The stored correct answer matches this result.