Topic: Interference and Young's double-slit experiment· Optics

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…

In Young's double slit experiment the separation d between the slits is 2 mm, the wavelength $\lambda$ 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 $0.20^\circ$. 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

1. 1.8 mm

2. 2.1 mm

3. 1.9 mm

4. 1.7 mm

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Answer: 3. 1.9 mm

Angular fringe width is $\theta=\dfrac{\lambda}{d}$, so $\theta\propto\dfrac1d$ for fixed $\lambda$.

$$\frac{d_2}{d_1}=\frac{\theta_1}{\theta_2}\Rightarrow d_2=2\times\frac{0.20}{0.21}\approx1.9\ \mathrm{mm}$$

The slit separation must be decreased to about 1.9 mm to increase the angular width.

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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…

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