Rankers Physics

Young's Double Slit Experiment: Practice Problem & Solution

In Young's double slit experiment the separation d between the slits is 2 mm, the wavelength $\lambda$ of the light used is $5896 AA$ and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is $0.20^\circ$. To increase the fringe angular width to $0.21^\circ$ (with same $\lambda$ and D) the separation between the slits needs to be changed to (2018)
2.1 mm
1.9 mm
1.8 mm
1.7 mm

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Young's Double Slit Experiment. Understanding the underlying formula is key to arriving at the correct answer below:

The angular fringe width is $\theta = \frac{\lambda}{d}$, which means $\theta \propto \frac{1}{d}$. So, $\theta_1 d_1 = \theta_2 d_2$. Substituting the values: $0.20 \times 2 = 0.21 \times d_2$. This yields $d_2 = \frac{0.40}{0.21} \approx 1.9 mm$.

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