In Young's double slits experiment, the position of $5^{\text {th }}$ bright fringe from the central maximum is $5 \,cm$ The distance between slits and screen is $1 \,m$ and wavelength of used monochromatic light is $600 \,mm$ The separation between the slits is:
- $12\, \mu m$
- $60\, \mu m$
- $36\, \mu m$
- $48 \,\mu m$
The Correct Option is D
Solution and Explanation
1. The position of bright fringes in Young's double-slit experiment is given by: \[ y_n = \frac{n \lambda D}{d}, \] where \(n\) is the fringe order, \(\lambda\) is the wavelength of light, \(D\) is the distance between the slits and screen, and \(d\) is the distance between the slits.
2. Substituting the given values: - \(n = 5, \, \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m}, \, y_n = 5 \, \text{cm} = 5 \times 10^{-2} \, \text{m}, \, D = 1 \, \text{m}\).
3. Rearrange for \(d\): \[ d = \frac{n \lambda D}{y_n}. \]
4. Substituting: \[ d = \frac{5 \times 600 \times 10^{-9} \times 1}{5 \times 10^{-2}} = 6 \times 10^{-6} \, \text{m} = 48 \, \mu\text{m}. \]
Thus, the distance between the slits is 48 \(\mu\text{m}\).
The fringe spacing depends on the wavelength, the slit-to-screen distance, and the slit separation. Accurate calculations require converting all quantities to SI units.
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Concepts Used:
Wave Optics
- Wave optics are also known as Physical optics which deal with the study of various phenomena such as polarization, interference, diffraction, and other occurrences where ray approximation of geometric optics cannot be done. Thus, the section of optics that deals with the behavior of light and its wave characteristics is known to be wave optics.
- In wave optics, the approximation is carried out by utilizing ray optics for the estimation of the field on a surface. Further, it includes integrating a ray-estimated field over a mirror, lens, or aperture for the calculation of the transmitted or scattered field.
- Wave optics stands as a witness to a famous standoff between two great scientific communities who devoted their lives to understanding the nature of light. Overall, one supports the particle nature of light; the other supports the wave nature.
- Sir Isaac Newton stood as a pre-eminent figure that supported the voice of particle nature of light, he proposed a corpuscular theory which states that “light consists of extremely light and tiny particles, called corpuscles which travel with very high speeds from the source of light to create a sensation of vision by reflecting on the retina of the eye”.