A : In Young.s double slit expriment the band width for red colour is more
R : Wavelength of red is small among the colours of white light.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of A
C. A is true and R is false
D. Both A and R are false

Answer

To solve the question, we need to analyze the statements provided:

**Statement A**: In Young's double slit experiment, the bandwidth for red color is more.
**Statement R**: The wavelength of red is small among the colors of white light.

### Step 1: Understanding the Bandwidth in Young's Double Slit Experiment
In Young's double slit experiment, the bandwidth (β) or fringe width is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \beta \) = fringe width
- \( \lambda \) = wavelength of light
- \( D \) = distance from the slits to the screen
- \( d \) = distance between the slits

### Step 2: Analyzing the Wavelength of Red Light
Among the colors of visible light, red light has the longest wavelength. The wavelengths of visible light range approximately from 400 nm (violet) to 700 nm (red). Therefore, red light has a larger wavelength compared to other colors.

### Step 3: Relating Wavelength to Bandwidth
Since the fringe width (β) is directly proportional to the wavelength (λ), this means:
- If the wavelength increases, the fringe width also increases.

### Step 4: Conclusion about Statement A
Since red light has the longest wavelength, it will produce a larger fringe width compared to other colors. Therefore, **Statement A is true**.

### Step 5: Conclusion about Statement R
Statement R claims that the wavelength of red light is small among the colors of white light, which is incorrect. Red light has the largest wavelength in the visible spectrum. Therefore, **Statement R is false**.

### Final Conclusion
- Statement A is true.
- Statement R is false.

### Summary
- A: True
- R: False