A: In the wave picture of light, intensity of light is determined by the square of the amplitude of the wave.
R: In the photon picture of light, for a given frequency, intensity of light is determined by the numberof photons per unit area.

Options

A. IF both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark(2)
C. IF Assertion is true statement but Reason is false then mark(3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the given question, we need to analyze both the assertion (A) and the reason (R) provided in the context of wave optics and the photon theory of light.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "In the wave picture of light, intensity of light is determined by the square of the amplitude of the wave."
- This is based on the principle that intensity (I) is proportional to the square of the amplitude (A) of the wave. Mathematically, this can be expressed as:
\[ I \propto A^2 \]
- Therefore, the assertion is correct.

2. **Understanding the Reason (R)**:
- The reason states that "In the photon picture of light, for a given frequency, intensity of light is determined by the number of photons per unit area."
- In the photon theory, intensity is related to the energy carried by photons. The energy of a single photon is given by:
\[ E = h \cdot f \]
where \(h\) is Planck's constant and \(f\) is the frequency of the light.
- The intensity can be expressed in terms of the number of photons (N) falling on a unit area per unit time (t):
\[ I = \frac{N \cdot E}{A \cdot t} = \frac{N \cdot h \cdot f}{A \cdot t} \]
- Thus, the intensity is indeed proportional to the number of photons per unit area per unit time, making the reason correct.

3. **Analyzing the Relationship**:
- Although both the assertion and reason are correct, we need to determine if there is a connection between them.
- The assertion discusses intensity in the wave model, while the reason discusses intensity in the photon model. They describe different perspectives on the same phenomenon but do not directly relate to each other.
- Therefore, while both statements are true, there is no direct connection between the assertion and the reason.

4. **Conclusion**:
- Since both the assertion and the reason are correct, but there is no connection between them, the correct answer is option 2.