## Core Concept
The concept being tested here is the relationship between distance from a radiation source and the effective dose received, which is governed by the **inverse square law**. This law states that the intensity of radiation (or dose) is inversely proportional to the square of the distance from the source. This principle is crucial in radiology and radiation protection.

## Why the Correct Answer is Right
Given that the effective dose at 1 meter (m) is 4 Gy, we can calculate the effective dose at 4 meters using the inverse square law. The formula based on this law is (D_2 = D_1 times left(frac{d_1}{d_2}right)^2), where (D_1) and (D_2) are the doses at distances (d_1) and (d_2), respectively. Substituting the given values: (D_1 = 4) Gy at (d_1 = 1) m, and (d_2 = 4) m, we get (D_2 = 4 times left(frac{1}{4}right)^2 = 4 times frac{1}{16} = 4 times 0.0625 = 0.25) Gy. Therefore, the effective dose at 4 meters is 0.25 Gy.

## Why Each Wrong Option is Incorrect
- **Option A:** This option suggests a direct relationship or no change, which contradicts the inverse square law.
- **Option B:** This option suggests a linear decrease with distance, which is incorrect according to the inverse square law.
- **Option D:** This option suggests an increase in dose with distance, which is the opposite of what the inverse square law states.

## Clinical Pearl / High-Yield Fact
A key point to remember is that as you move away from a radiation source, the dose you receive decreases with the square of the distance. This is why **doubling the distance from a radiation source reduces the dose to one-fourth**. This principle is vital for radiation protection in medical settings.

## Correct Answer Line
**Correct Answer: C. 0.25 Gy.**