In the laboratory, diffraction of light by a single slit is being observed. If slit is made slightly narrow, then diffraction pattern will-

Options

A. be more spreaded than before
B. be less spreaded than before
C. be spreaded as before
D. be disappeared

Answer

To solve the problem regarding the effect of narrowing a single slit on the diffraction pattern, we can follow these steps:

### Step 1: Understand the Diffraction Pattern
When light passes through a single slit, it creates a diffraction pattern on a screen. This pattern consists of a central maximum (bright fringe) and several minima and maxima on either side.

**Hint:** Remember that the diffraction pattern is influenced by the width of the slit.

### Step 2: Identify the Relationship Between Slit Width and Diffraction
The width of the slit (denoted as 'd') is inversely related to the spread of the diffraction pattern. This means that as the slit width decreases, the diffraction pattern becomes wider.

**Hint:** Think about how changing the slit width affects the angles at which minima occur.

### Step 3: Analyze the Condition for Minima
The condition for the formation of minima in a single slit diffraction pattern is given by:
\[ d \sin \theta = m \lambda \]
where \( m \) is the order of the minima, \( \lambda \) is the wavelength of the light, and \( \theta \) is the angle of diffraction.

**Hint:** Consider what happens to the angle \( \theta \) when the slit width 'd' is decreased.

### Step 4: Calculate the Spread of the Central Maximum
The distance between two consecutive minima (or maxima) can be expressed as:
\[ y = \frac{\lambda D}{d} \]
where \( D \) is the distance from the slit to the screen. This shows that the distance 'y' is directly proportional to the wavelength \( \lambda \) and the distance \( D \), and inversely proportional to the slit width 'd'.

**Hint:** How does changing 'd' affect the value of 'y'?

### Step 5: Conclusion
Since the slit is made narrower (decreasing 'd'), the distance 'y' between the minima increases, leading to a more spread out diffraction pattern. Therefore, the correct conclusion is that the diffraction pattern will become more spread out.

**Hint:** Relate your conclusion back to the initial question about the effect of narrowing the slit on the diffraction pattern.

### Final Answer
If the slit is made slightly narrower, the diffraction pattern will become more spread out.