A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young's double-slit experiment.
What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?

Solution

Here, a beam of light consists of two wavelengths.

Wavelength, $λ_{1} = 650 nm = 650 \times 10^{- 9} m$
Wavelength, $λ_{2} = 520 nm = 520 \times 10^{- 9} m$

Suppose, $d = distance between two slits$
$D = distance of screen from the slits .$

Let n fringes of wavelength 650 nm coincide with (n + 1) fringes of wavelength 520 nm.

$x = {nλ}_{1} D / d = (n + 1) λ_{2} D / d$

$\Rightarrow$ $x = n \times 650 = (n + 1) \times 520$

$\Rightarrow$ $\frac{n + 1}{n} = \frac{650}{520} = \frac{5}{4}$

$\Rightarrow$ $1 + \frac{1}{n} = \frac{5}{4} \Rightarrow \frac{1}{n} = \frac{5}{4} - 1 = \frac{1}{4}$

$\Rightarrow$ $n = 4$
Hence,
Distance from the central maximum, $x = n . λ_{1} \frac{D}{d}$
$= 4 \times 650 \times 10^{- 7} \times \frac{120}{0.2} = 1.56 mm .$

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Wave Optics

A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young's double-slit experiment.
What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?

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Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

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For Daily Free Study Material Join wiredfaculty

Wave Optics

A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young's double-slit experiment.What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?

Some More Questions From Wave Optics Chapter

Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young's double-slit experiment.
What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?