A spherical surface of radius 30 cm separates two transparent media A and B with refractive indices 1'33 and 1.48 respectively. The medium A is on the convex side of the surface. Where should a point object be placed in medium A so that the paraxial rays become parallel after refraction at the surface ?

Explanation

To solve the problem, we need to determine the position of a point object in medium A such that the paraxial rays become parallel after refraction at the spherical surface separating the two media.

### Step-by-Step Solution:

1. **Identify Given Values**:
- Radius of curvature (R) = 30 cm (since the medium A is on the convex side, R is positive).
- Refractive index of medium A (μ1) = 1.33.
- Refractive index of medium B (μ2) = 1.48.

2. **Understand the Condition for Parallel Rays**:
- For the rays to become parallel after refraction, they must converge to infinity. This means that the image formed (v) is at infinity.

3. **Use the Refraction Formula**:
- The formula relating the refractive indices and distances is given by:
\[ \frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R} \]
- Here, \( v = \infty \), so \( \frac{\mu_2}{v} = 0 \).

4. **Substitute the Known Values**:
- Substitute the known values into the equation:
\[ 0 - \frac{1.33}{u} = \frac{1.48 - 1.33}{30} \]
- Simplifying the right side:
\[ 0 - \frac{1.33}{u} = \frac{0.15}{30} \]
- This simplifies to:
\[ -\frac{1.33}{u} = 0.005 \]

5. **Solve for u**:
- Rearranging gives:
\[ \frac{1.33}{u} = 0.005 \]
- Thus,
\[ u = \frac{1.33}{0.005} = 266 \text{ cm} \]
- Since we are considering the sign convention, the object distance \( u \) will be negative (as per the sign convention for distances measured against the direction of incident light):
\[ u = -266 \text{ cm} \]

6. **Conclusion**:
- The point object should be placed at a distance of 266 cm in medium A from the spherical surface.

### Final Answer:
The point object should be placed at \( -266 \) cm in medium A.