Question

In Young’s double slit experiment the separation d between the slits is 2 mm, the wavelength λ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20°. To increase the fringe angular width to 0.21° (with same λ and D) the separation between the slits needs to be changed to

• A. 1.8mm
• B. 2.1mm
• C. 1.9mm
• D. 1.7mm

Answer 1

The Correct Option is C

To solve this problem, we use the relation for angular fringe width in Young's double-slit experiment:

\[ \theta = \frac{\lambda}{d} \]

Given:

• \( d_1 = 2\,\text{mm} = 2 \times 10^{-3}\,\text{m} \)
• \( \lambda = 5896\,\text{\AA} = 5896 \times 10^{-10}\,\text{m} \)
• \( \theta_1 = 0.20^\circ \)
• \( \theta_2 = 0.21^\circ \)

Since \( \lambda \) is constant:

\[ \frac{\theta_2}{\theta_1} = \frac{d_1}{d_2} \]

\[ \frac{0.21}{0.20} = \frac{2}{d_2} \]

\[ d_2 = \frac{2 \times 0.20}{0.21} = \frac{40}{21}\,\text{mm} \approx 1.90\,\text{mm} \]

Final Answer: \( 1.9\,\text{mm} \)