Assertion: if wavelength of light is doubled, energy and momentum of photons are reduced to half.
Reason: By increasing the wavelength, speed of photons will decrease.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason or true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to evaluate the assertion and reason provided and determine their validity based on the principles of physics.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that if the wavelength of light is doubled, the energy and momentum of photons are reduced to half.
- The energy \( E \) of a photon is given by the formula:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength.
- The momentum \( P \) of a photon is given by:
\[ P = \frac{h}{\lambda} \]
- From these formulas, we can see that both energy and momentum are inversely proportional to the wavelength \( \lambda \).

2. **Analyzing the Effect of Doubling the Wavelength**:
- If the wavelength \( \lambda \) is doubled (i.e., \( \lambda' = 2\lambda \)):
- The new energy \( E' \) becomes:
\[ E' = \frac{hc}{\lambda'} = \frac{hc}{2\lambda} = \frac{1}{2} \left( \frac{hc}{\lambda} \right) = \frac{1}{2} E \]
- The new momentum \( P' \) becomes:
\[ P' = \frac{h}{\lambda'} = \frac{h}{2\lambda} = \frac{1}{2} \left( \frac{h}{\lambda} \right) = \frac{1}{2} P \]
- Therefore, if the wavelength is doubled, both the energy and momentum are indeed reduced to half. Thus, the assertion is **true**.

3. **Understanding the Reason**:
- The reason states that by increasing the wavelength, the speed of photons will decrease.
- However, it is a fundamental property of photons that they always travel at the speed of light \( c \) in a vacuum, regardless of their wavelength.
- Therefore, the reason is **false**.

4. **Conclusion**:
- Since the assertion is true and the reason is false, the correct option is that the assertion is true, but the reason is false.

### Final Answer:
The correct answer is that the assertion is true and the reason is false.