In Young’s double slit experiment using a source of wavelength \(\lambda\) interference bands are observed on a screen. If the separation between the slits alone is halved in this experiment, then the angular separation \(\omega\) of the fringes on the screen becomes
\(2\omega\)
Angular fringe separation: \(\omega = \dfrac{\lambda}{d}\)
Slit separation is halved: \(d' = \dfrac{d}{2}\)
\(\omega' = \dfrac{\lambda}{d/2} = \dfrac{2\lambda}{d} = 2\omega\)
Hence, \(2\omega\).
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- In a Young's double slit experiment set up, the two slits are kept $0.4\text{ mm}$ apart and screen is placed at $1\text{ m}$ from slits. If a thin transparent sheet of thickness $20 \, \mu\text{m}$ is introduced in front of one of the slits then center bright fringe shifts by $20\text{ mm}$ on the screen. The refractive index of transparent sheet is given by $\frac{\alpha}{10}$, where $\alpha$ is __________.
- In two separate Young's double-slit experimental set-ups and two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slits separations and that of the wavelengths of light used are $2 : 1$ and $1 : 2$ respectively. The corresponding ratio of the distances between the slits and the respective screens ($D_1/D_2$) is ___________.
- The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions $8 \text{ cm}$ and $24 \text{ cm}$ from the lens. The focal length of the lens is ________ $\text{cm}$.
- A ray of light travelling in air is incident on one face of a parallel glass slab of thickness $t$ and refractive index $\mu$ at an angle of incidence $i$. Total time spent by the ray inside the slab is
