A beam of light consisting of two wavelengths 7000 and 5500 is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is 2.5 mm and the distance between the plane of slits and the screen is 150 cm. [2023

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Solution

Q.
A beam of light consisting of two wavelengths 7000 $Å$ and 5500 $Å$ is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is 2.5 mm and the distance between the plane of slits and the screen is 150 cm. The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is $n \times 10^{- 5} m$ . The value of $n$ is _______. [2023]

Ans.
(462)

$d = 2.5 mm, D = 150 cm$

$Fringe width β = \frac{λ D}{d}$

$Let n^{th} bright fringe of λ_{1} match with m^{th} bright fringe of λ_{2}$

$\Rightarrow n β_{1} = m β_{2}$

$\Rightarrow n λ_{1} = m λ_{2} \Rightarrow \frac{n}{m} = \frac{λ_{2}}{λ_{1}} = \frac{5500}{7000}$

$\Rightarrow \frac{n}{m} = \frac{11}{14}$

$Distance where bright fringe will match$

$= n β_{1} = \frac{11 \times 7000 Å \times 150 cm}{0.25 cm} = 462 \times 10^{- 5}$

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