Read the paragraph and chose the correct answer of the...

Read the paragraph and chose the correct answer of the following questions In young experiment position of bright fringes is given by $\mathrm{x}=\mathrm{n} \lambda(\mathrm{D} / \mathrm{d})$ and the position of dark fringes is given by $\mathrm{x}=(2 \mathrm{n}-1)(N 2)(\mathrm{D} / \mathrm{d})$ where $\mathrm{n}=1,2,3 \ldots \ldots \ldots \ldots$ for first second, third bright/dark fringe. The center of the fringe pattern is bright (for $\mathrm{n}=0$ ). The width of each bright/dark fringe is $\beta=(\lambda \mathrm{D} / \mathrm{d})$, Where $\lambda=5000 \AA$. Slits are $0.2 \mathrm{~cm}$ apart and $\mathrm{D}=1 \mathrm{~m}$ (i) If light of wavelength $6000 \AA$ be used in the above experiment the fringe width would be $\mathrm{mm}$ (A) $0.30$ (B) 3 (C) $0.6$ (D) 6 (ii) with the light of wavelength $5000 \AA$, If experiment were carried out under water of a $n=(4 / 3)$ the fringe width would be (A) zero (B) $(4 / 3)$ times (C) (3/4) times (D) none of these

Read the paragraph and chose the correct answer of the following questions In young experiment position of bright fringes is given by $\mathrm{x}=\mathrm{n} \lambda(\mathrm{D} / \mathrm{d})$ and the position of dark fringes is given by $\mathrm{x}=(2 \mathrm{n}-1)(N 2)(\mathrm{D} / \mathrm{d})$ where $\mathrm{n}=1,2,3 \ldots \ldots \ldots \ldots$ for first
second, third bright/dark fringe. The center of the fringe pattern is bright (for $\mathrm{n}=0$ ). The width of each bright/dark fringe is $\beta=(\lambda \mathrm{D} / \mathrm{d})$, Where $\lambda=5000 \AA$. Slits are $0.2 \mathrm{~cm}$
apart and $\mathrm{D}=1 \mathrm{~m}$
(i) If light of wavelength $6000 \AA$ be used in the above experiment the fringe width would be $\mathrm{mm}$
(A) $0.30$
(B) 3
(C) $0.6$
(D) 6
(ii) with the light of wavelength $5000 \AA$, If experiment were carried out under water of a $n=(4 / 3)$ the fringe width would be
(A) zero
(B) $(4 / 3)$ times
(C) (3/4) times
(D) none of these

Key Concepts

Young's Double Slit Experiment

This fundamental physics experiment demonstrates the wave nature of light by splitting a coherent light source into two beams that interfere with each other, producing an interference pattern of bright and dark fringes on a screen. The pattern arises from constructive and destructive interference resulting from differences in the paths traveled by the light from each slit.

Interference Fringe Formation

Interference fringe formation refers to the creation of alternating bright and dark bands due to the phase difference between two coherent light waves. Constructive interference leads to bright fringes when the path difference is an integer multiple of the wavelength, while destructive interference leads to dark fringes when the path difference is an odd multiple of half the wavelength.

Fringe Spacing

Fringe spacing, or the width of each bright or dark fringe, is a measure of the distance between successive interference fringes and depends on the wavelength of the light, the distance from the slits to the screen, and the separation of the slits. It quantifies the scale of the interference pattern produced in experiments like Young's double slit setup.

Effect of Medium on Wavelength

When light propagates through a medium with a refractive index different from that of vacuum, its wavelength changes according to the medium's refractive index (wavelength in medium equals wavelength in vacuum divided by the refractive index). This alteration in wavelength directly affects the spacing of interference fringes in an experiment by compressing or expanding the fringe pattern compared to that in air or vacuum.

Transcript

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