Both in interference and diffraction phenomena, alternate dark and bright fringes are obtained on screen
I) generally fringe width is same in interference and not same in diffraction
II) the central fringe in interference has maximum brightness and the intensity gradually decreases on either side
III) in interference the intensity of all bright fringes is same
IV) both the phenomena are produced from same coherent sources.

Options

A. I only
B. I and II
C. I, II and IV
D. I, III and IV

Answer

To analyze the statements regarding interference and diffraction phenomena, let's evaluate each statement step by step.

### Step 1: Evaluate Statement I
**Statement I**: "Generally fringe width is same in interference and not same in diffraction."

- In interference, the fringe width (β) is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where \( \lambda \) is the wavelength of light, \( D \) is the distance from the slits to the screen, and \( d \) is the distance between the slits. This fringe width remains constant for all fringes.

- In diffraction, particularly single-slit diffraction, the fringe width is not constant and varies, especially for the central maximum which is wider than the other fringes.

**Conclusion**: Statement I is correct.

### Step 2: Evaluate Statement II
**Statement II**: "The central fringe in interference has maximum brightness and the intensity gradually decreases on either side."

- In interference patterns, the central fringe is indeed the brightest, but the intensity of all bright fringes remains the same. The intensity does not gradually decrease on either side in interference; it is uniform for all bright fringes.

**Conclusion**: Statement II is incorrect.

### Step 3: Evaluate Statement III
**Statement III**: "In interference, the intensity of all bright fringes is the same."

- As stated, in interference patterns created by two coherent sources, all bright fringes have the same intensity due to the constructive interference of light waves.

**Conclusion**: Statement III is correct.

### Step 4: Evaluate Statement IV
**Statement IV**: "Both the phenomena are produced from same coherent sources."

- For both interference and diffraction to occur, the light sources must be coherent, meaning they have a constant phase difference and the same frequency. This is essential for producing stable interference patterns.

**Conclusion**: Statement IV is correct.

### Final Summary
The correct statements are:
- Statement I: Correct
- Statement II: Incorrect
- Statement III: Correct
- Statement IV: Correct

Thus, the correct options are I, III, and IV.