Question

In Young’s double-slit experiment, the slit separation is 0.4 mm and the screen is 2 m away. If light of wavelength 600 nm is used, the fringe width is:

• A. 2 mm
• B. 3 mm
• C. 4 mm
• D. 5 mm

Hint:

Always convert all physical quantities to their standard SI units (meters) before performing calculations.
Conversion factors:
$1\text{ nm} = 10^{-9}\text{ m}$
$1\text{ mm} = 10^{-3}\text{ m}$
Keeping the powers of 10 sorted makes calculations straightforward and error-free.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question belongs to the topic "Wave Optics," focusing on the interference of light in Young's Double Slit Experiment (YDSE).
We are required to compute the fringe width ($\beta$) using the given slit separation, distance of the screen from the slits, and wavelength of the light.

Step 2: Key Formula or Approach:
The fringe width ($\beta$) in Young's Double Slit Experiment is calculated using:
\[ \beta = \frac{\lambda D}{d} \]
where:
$\lambda$ = wavelength of light used
$D$ = distance between the slits and the screen
$d$ = slit separation (distance between the two coherent sources)

Step 3: Detailed Explanation:

• We are given the following values:
Slit separation ($d$) = $0.4\text{ mm} = 0.4 \times 10^{-3}\text{ m}$
Distance of screen ($D$) = $2\text{ m}$
Wavelength of light ($\lambda$) = $600\text{ nm} = 600 \times 10^{-9}\text{ m} = 6 \times 10^{-7}\text{ m}$

• Substitute these values in the fringe width equation:
\[ \beta = \frac{(6 \times 10^{-7}\text{ m}) \times (2\text{ m})}{0.4 \times 10^{-3}\text{ m}} \]

• Simplify the numerator:
\[ 6 \times 10^{-7} \times 2 = 1.2 \times 10^{-6}\text{ m}^2 \]

• Simplify the denominator:
\[ 0.4 \times 10^{-3} = 4 \times 10^{-4}\text{ m} \]

• Calculate the final value of $\beta$:
\[ \beta = \frac{1.2 \times 10^{-6}}{4 \times 10^{-4}} = 0.3 \times 10^{-2}\text{ m} = 3 \times 10^{-3}\text{ m} \]

• Convert the answer from meters to millimeters:
\[ \beta = 3\text{ mm} \]



Step 4: Final Answer:
The fringe width is $3\text{ mm}$, which is option (B).