In a double slit interference pattern, the first maxima for infrared light would be

Options

A. at the same place as the first maxima for green light
B. closer to the centre than the first maxima for green light
C. farther from the centre than the first maxima for green light
D. infrared light does not produce an interference pattern

Answer

To solve the problem regarding the first maxima in a double slit interference pattern for infrared light, we will follow these steps:

### Step 1: Understand the Concept of Double Slit Interference
In a double slit interference pattern, light waves passing through two closely spaced slits interfere with each other, creating a pattern of bright and dark fringes on a screen. The bright fringes (maxima) occur where the waves from the two slits arrive in phase.

**Hint:** Remember that maxima occur at points where the path difference between the two waves is an integer multiple of the wavelength.

### Step 2: Identify the Wavelength of Infrared Light
Infrared light has a wavelength range of approximately 700 nm to 1 mm (or 1,000,000 nm). For calculations, we will consider the lower end of the range, which is 700 nm.

**Hint:** Always check the wavelength range of the light being used in interference experiments.

### Step 3: Use the Formula for Fringe Width
The fringe width (β) in a double slit experiment is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) is the wavelength of the light,
- \( D \) is the distance from the slits to the screen,
- \( d \) is the distance between the slits.

For the first maxima (n=1), the formula simplifies to:
\[ \beta = \frac{\lambda D}{d} \]

**Hint:** Remember that for the first maxima, we consider n=1 in the formula.

### Step 4: Compare with Green Light
Green light has a wavelength range of approximately 500 nm to 570 nm. For comparison, we can take an average value of around 560 nm.

Since the wavelength of infrared light (700 nm) is greater than that of green light (560 nm), we can conclude that the fringe width for infrared light will be greater than that for green light.

**Hint:** When comparing wavelengths, remember that a longer wavelength results in a larger fringe width.

### Step 5: Conclusion
Since the fringe width for infrared light is greater than that for green light, the first maxima for infrared light will be located further from the center than the first maxima for green light.

Thus, the correct answer is that the first maxima for infrared light lies further from the center than the first maxima for green light.

**Final Answer:** The first maxima for infrared light would be further from the center than the first maxima for green light.