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 determine the new slit separation for increased angular fringe width in Young’s double slit experiment:

Angular fringe width is given by:

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

Given:

• \( \lambda = 5896\,\text{\AA} = 5896 \times 10^{-10}\,\text{m} \)

Initial condition:

\[ \theta_1 = 0.20^\circ = 0.20 \times \frac{\pi}{180} = \frac{\pi}{900}\,\text{rad} \]

\[ d_1 = \frac{\lambda}{\theta_1} = \frac{5896 \times 10^{-10}}{\pi/900} \approx 2 \times 10^{-3}\,\text{m} = 2\,\text{mm} \]

New condition:

\[ \theta_2 = 0.21^\circ = 0.21 \times \frac{\pi}{180} = \frac{7\pi}{6000}\,\text{rad} \]

\[ d_2 = \frac{\lambda}{\theta_2} = \frac{5896 \times 10^{-10}}{7\pi/6000} \approx 1.9 \times 10^{-3}\,\text{m} = 1.9\,\text{mm} \]

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