Question

In Young's double slit experiment, when light of wavelength $600\text{ nm}$ is used, 18 fringes are observed on the screen. If the wavelength of light is changed to $400\text{ nm}$ , the number of fringes observed on the screen is

• A. 12
• B. 27
• C. 22
• D. 24

Hint:

$n \propto 1/\lambda$. If wavelength decreases by a factor of $1.5$ ($600/400$), the number of fringes must increase by a factor of $1.5$ ($18 \times 1.5 = 27$).

Answer 1

The Correct Option is B

Step 1: Concept
For a fixed length of the screen ($L$), the number of fringes ($n$) and wavelength ($\lambda$) are related by $L = n_1 \beta_1 = n_2 \beta_2$, which simplifies to $n_1 \lambda_1 = n_2 \lambda_2$.

Step 2: Meaning
Smaller wavelengths produce narrower fringes, allowing more of them to fit in the same space.

Step 3: Analysis
$18 \times 600 = n_2 \times 400$
$n_2 = \frac{18 \times 600}{400} = \frac{18 \times 6}{4}$
$n_2 = \frac{108}{4} = 27$.

Step 4: Conclusion
The number of fringes observed is 27. Final Answer: (B)